Topology最新文献

{"title":"Information for Authors","authors":"","doi":"10.1016/S0040-9383(07)00042-0","DOIUrl":"https://doi.org/10.1016/S0040-9383(07)00042-0","url":null,"abstract":"","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 4","pages":"Page IFC"},"PeriodicalIF":0.0,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0040-9383(07)00042-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"137353186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The length of a shortest geodesic net on a closed Riemannian manifold","authors":"Regina Rotman","doi":"10.1016/j.top.2006.10.003","DOIUrl":"10.1016/j.top.2006.10.003","url":null,"abstract":"<div><p>In this paper we will estimate the smallest length of a minimal geodesic net on an arbitrary closed Riemannian manifold <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> in terms of the diameter of this manifold and its dimension. Minimal geodesic nets are critical points of the length functional on the space of immersed graphs into a Riemannian manifold. We prove that there exists a minimal geodesic net that consists of <span><math><mi>m</mi></math></span> geodesics connecting two points <span><math><mi>p</mi><mo>,</mo><mi>q</mi><mo>∈</mo><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> of total length <span><math><mo>≤</mo><mi>m</mi><mi>d</mi></math></span>, where <span><math><mi>m</mi><mo>∈</mo><mrow><mo>{</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>}</mo></mrow></math></span> and <span><math><mi>d</mi></math></span> is the diameter of <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. We also show that there exists a minimal geodesic net with at most <span><math><mi>n</mi><mo>+</mo><mn>1</mn></math></span> vertices and <span><math><mfrac><mrow><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> geodesic segments of total length <span><math><mo>≤</mo><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mstyle><mi>FillRad</mi></mstyle><mspace></mspace><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>≤</mo><msup><mrow><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>n</mi></mrow><mrow><mi>n</mi></mrow></msup><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><msqrt><mrow><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mi>!</mi></mrow></msqrt><mstyle><mi>vol</mi></mstyle><msup><mrow><mrow><mo>(</mo><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msup></math></span>.</p><p>These results significantly improve one of the results of [A. Nabutovsky, R. Rotman, The minimal length of a closed geodesic net on a Riemannian manifold with a nontrivial second homology group, Geom. Dedicata 113 (2005) 234–254] as well as most of the results of [A. Nabutovsky, R. Rotman, Volume, diameter and the minimal mass of a stationary 1-cycle, Geom. Funct. Anal. 14 (4) (2004) 748–790].</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 4","pages":"Pages 343-356"},"PeriodicalIF":0.0,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.10.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Evaluation maps in rational homotopy","authors":"Yves Félix ,&nbsp;Gregory Lupton","doi":"10.1016/j.top.2007.03.005","DOIUrl":"10.1016/j.top.2007.03.005","url":null,"abstract":"<div><p>In the rational category of nilpotent complexes, let <span><math><mi>E</mi></math></span> be an <span><math><mi>H</mi></math></span>-space acting on a space <span><math><mi>X</mi></math></span>. With mild hypotheses we show that the action on the base point <span><math><mstyle><mi>w</mi></mstyle><mo>:</mo><mi>E</mi><mo>→</mo><mi>X</mi></math></span> factors through a map <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>E</mi></mrow></msub><mo>:</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>E</mi></mrow></msub><mo>→</mo><mi>X</mi></math></span>, where <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>E</mi></mrow></msub></math></span> is a finite product of odd-dimensional spheres and <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mi>E</mi></mrow></msub></math></span> is a homotopy monomorphism. Among others, the following consequences are obtained: <span><math><msub><mrow><mi>π</mi></mrow><mrow><mo>∗</mo></mrow></msub><mrow><mo>(</mo><mstyle><mi>w</mi></mstyle><mo>)</mo></mrow><mo>≠</mo><mn>0</mn></math></span> if and only if <span><math><mstyle><mi>w</mi></mstyle></math></span> is essential and <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>∗</mo></mrow></msub><mrow><mo>(</mo><mstyle><mi>w</mi></mstyle><mo>)</mo></mrow><mo>≠</mo><mn>0</mn></math></span> if and only if <span><math><mi>X</mi></math></span> satisfies a strong splitting condition.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 5","pages":"Pages 493-506"},"PeriodicalIF":0.0,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2007.03.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Poincaré invariants","authors":"Markus Dürr,&nbsp;Alexandre Kabanov,&nbsp;Christian Okonek","doi":"10.1016/j.top.2007.02.004","DOIUrl":"10.1016/j.top.2007.02.004","url":null,"abstract":"<div><p>We construct an obstruction theory for relative Hilbert schemes in the sense of [K. Behrend, B. Fantechi, The intrinsic normal cone, Invent. Math. 128 (1) (1997) 45–88] and compute it explicitly for relative Hilbert schemes of divisors on smooth projective varieties. In the special case of curves on a surface <span><math><mi>V</mi></math></span>, our obstruction theory determines a virtual fundamental class <span><math><mrow><mo>[</mo><mrow><mo>[</mo><msubsup><mrow><mstyle><mi>Hilb</mi></mstyle></mrow><mrow><mi>V</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>]</mo></mrow><mo>]</mo></mrow><mo>∈</mo><msub><mrow><mi>A</mi></mrow><mrow><mfrac><mrow><mi>m</mi><mrow><mo>(</mo><mi>m</mi><mo>−</mo><mi>k</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msub><mrow><mo>(</mo><msubsup><mrow><mstyle><mi>Hilb</mi></mstyle></mrow><mrow><mi>V</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>)</mo></mrow></math></span>, which we use to define Poincaré invariants <span><span><span><math><mrow><mo>(</mo><msubsup><mrow><mi>P</mi></mrow><mrow><mi>V</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>P</mi></mrow><mrow><mi>V</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>)</mo></mrow><mo>:</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>V</mi><mo>,</mo><mi>Z</mi><mo>)</mo></mrow><mo>⟶</mo><msup><mrow><mi>Λ</mi></mrow><mrow><mo>∗</mo></mrow></msup><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>V</mi><mo>,</mo><mi>Z</mi><mo>)</mo></mrow><mo>×</mo><msup><mrow><mi>Λ</mi></mrow><mrow><mo>∗</mo></mrow></msup><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>V</mi><mo>,</mo><mi>Z</mi><mo>)</mo></mrow><mtext>.</mtext></math></span></span></span> These maps are invariant under deformations, satisfy a blow-up formula, and a wall crossing formula for surfaces with <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub><mrow><mo>(</mo><mi>V</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn></math></span>. For the case <span><math><mi>q</mi><mrow><mo>(</mo><mi>V</mi><mo>)</mo></mrow><mo>≥</mo><mn>1</mn></math></span>, we calculate the wall crossing formula explicitly in terms of fundamental classes of certain Brill–Noether loci for curves. We determine the invariants completely for ruled surfaces, and rederive from this classical results of Nagata and Lange. The invariant <span><math><mrow><mo>(</mo><msubsup><mrow><mi>P</mi></mrow><mrow><mi>V</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>P</mi></mrow><mrow><mi>V</mi></mrow><mrow><mo>−</mo></mrow></msubsup><mo>)</mo></mrow></math></span> of an elliptic fibration is computed in terms of its multiple fibers.</p><p>When the fibered product <span><math><msubsup><mrow><mstyle><mi>Hilb</mi></mstyle></mrow><mrow><mi>V</mi></mrow><mrow><mi>m</mi></mrow></msubsup><msub><mrow><mo>×</mo></mrow><mrow><msubsup><mrow><mstyle><mi>Pic</mi></mstyle></mrow><mrow><mi>V</mi>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 3","pages":"Pages 225-294"},"PeriodicalIF":0.0,"publicationDate":"2007-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2007.02.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"104537322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Information for Authors","authors":"","doi":"10.1016/S0040-9383(07)00034-1","DOIUrl":"https://doi.org/10.1016/S0040-9383(07)00034-1","url":null,"abstract":"","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 3","pages":"Page IFC"},"PeriodicalIF":0.0,"publicationDate":"2007-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0040-9383(07)00034-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91629300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Localization and completion of nilpotent groups of automorphisms","authors":"Ken-Ichi Maruyama","doi":"10.1016/j.top.2007.01.003","DOIUrl":"10.1016/j.top.2007.01.003","url":null,"abstract":"<div><p>We study nilpotent subgroups of automorphism groups in the category of groups and the homotopy category of spaces. We establish localization and completion theorems for nilpotent groups of automorphisms of nilpotent groups. We then apply these algebraic theorems to prove analogous results for certain groups of self-homotopy equivalences of spaces.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 3","pages":"Pages 319-341"},"PeriodicalIF":0.0,"publicationDate":"2007-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2007.01.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Torelli theorem for the moduli spaces of connections on a Riemann surface","authors":"Indranil Biswas ,&nbsp;Vicente Muñoz","doi":"10.1016/j.top.2007.02.005","DOIUrl":"https://doi.org/10.1016/j.top.2007.02.005","url":null,"abstract":"<div><p>Let <span><math><mrow><mo>(</mo><mi>X</mi><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></mrow></math></span> be any one-pointed compact connected Riemann surface of genus <span><math><mi>g</mi></math></span>, with <span><math><mi>g</mi><mo>≥</mo><mn>3</mn></math></span>. Fix two mutually coprime integers <span><math><mi>r</mi><mo>&gt;</mo><mn>1</mn></math></span> and <span><math><mi>d</mi></math></span>. Let <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> denote the moduli space parametrizing all logarithmic <span><math><mstyle><mi>SL</mi></mstyle><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>C</mi><mo>)</mo></mrow></math></span>-connections, singular over <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, on vector bundles over <span><math><mi>X</mi></math></span> of degree <span><math><mi>d</mi></math></span>. We prove that the isomorphism class of the variety <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> determines the Riemann surface <span><math><mi>X</mi></math></span> uniquely up to an isomorphism, although the biholomorphism class of <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> is known to be independent of the complex structure of <span><math><mi>X</mi></math></span>. The isomorphism class of the variety <span><math><msub><mrow><mi>M</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> is independent of the point <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><mi>X</mi></math></span>. A similar result is proved for the moduli space parametrizing logarithmic <span><math><mstyle><mi>GL</mi></mstyle><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>C</mi><mo>)</mo></mrow></math></span>-connections, singular over <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, on vector bundles over <span><math><mi>X</mi></math></span> of degree <span><math><mi>d</mi></math></span>. The assumption <span><math><mi>r</mi><mo>&gt;</mo><mn>1</mn></math></span> is necessary for the moduli space of logarithmic <span><math><mstyle><mi>GL</mi></mstyle><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>C</mi><mo>)</mo></mrow></math></span>-connections to determine the isomorphism class of <span><math><mi>X</mi></math></span> uniquely.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 3","pages":"Pages 295-317"},"PeriodicalIF":0.0,"publicationDate":"2007-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2007.02.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91629299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Symplectic symmetries of 4-manifolds","authors":"Weimin Chen ,&nbsp;Slawomir Kwasik","doi":"10.1016/j.top.2006.12.003","DOIUrl":"10.1016/j.top.2006.12.003","url":null,"abstract":"<div><p>A study of symplectic actions of a finite group <span><math><mi>G</mi></math></span> on smooth 4-manifolds is initiated. The central new idea is the use of <span><math><mi>G</mi></math></span>-equivariant Seiberg–Witten–Taubes theory in studying the structure of the fixed-point set of these symmetries. The main result in this paper is a complete description of the fixed-point set structure (and the action around it) of a symplectic cyclic action of prime order on a minimal symplectic 4-manifold with <span><math><msubsup><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>=</mo><mn>0</mn></math></span>. Comparison of this result with the case of locally linear topological actions is made. As an application of these considerations, the triviality of many such actions on a large class of 4-manifolds is established. In particular, we show the triviality of homologically trivial symplectic symmetries of a <span><math><mi>K</mi><mn>3</mn></math></span> surface (in analogy with holomorphic automorphisms). Various examples and comments illustrating our considerations are also included.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 2","pages":"Pages 103-128"},"PeriodicalIF":0.0,"publicationDate":"2007-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.12.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The discrete module category for the ring of K-theory operations","authors":"Francis Clarke ,&nbsp;Martin Crossley ,&nbsp;Sarah Whitehouse","doi":"10.1016/j.top.2007.01.001","DOIUrl":"10.1016/j.top.2007.01.001","url":null,"abstract":"<div><p>We study the category of discrete modules over the ring of degree-zero stable operations in <span><math><mi>p</mi></math></span>-local complex <span><math><mi>K</mi></math></span>-theory, where <span><math><mi>p</mi></math></span> is an odd prime. We show that the <span><math><msub><mrow><mi>K</mi></mrow><mrow><mrow><mo>(</mo><mi>p</mi><mo>)</mo></mrow></mrow></msub></math></span>-homology of any space or spectrum is such a module, and that this category is isomorphic to a category defined by Bousfield and used in his work on the <span><math><msub><mrow><mi>K</mi></mrow><mrow><mrow><mo>(</mo><mi>p</mi><mo>)</mo></mrow></mrow></msub></math></span>-local stable homotopy category. We give a simple construction of cofree discrete modules and construct the analogue in the category of discrete modules of a four-term exact sequence due to Bousfield.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 2","pages":"Pages 139-154"},"PeriodicalIF":0.0,"publicationDate":"2007-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2007.01.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Elliptic triangle groups in PU(2,1), Lagrangian triples and momentum maps","authors":"Julien Paupert","doi":"10.1016/j.top.2007.01.002","DOIUrl":"10.1016/j.top.2007.01.002","url":null,"abstract":"<div><p>We determine the possible eigenvalues of elliptic matrices <span><math><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi></math></span> in <span><math><mi>P</mi><mi>U</mi><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span> satisfying <span><math><mi>A</mi><mi>B</mi><mi>C</mi><mo>=</mo><mn>1</mn></math></span>. This is done by describing geometrically the image of a group-valued momentum map for the (non-compact) group action of <span><math><mi>P</mi><mi>U</mi><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span> by conjugation on <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>×</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> where <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> are fixed elliptic conjugacy classes in <span><math><mi>P</mi><mi>U</mi><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span>. Contrary to the compact case, this image is not always convex; rather it is the union of one, two or three convex polygons in <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>/</mo><msub><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. The main motivation was to analyze elliptic triangle groups in <span><math><mi>P</mi><mi>U</mi><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span> such as Mostow’s lattices.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 2","pages":"Pages 155-183"},"PeriodicalIF":0.0,"publicationDate":"2007-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2007.01.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}