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IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-10-01 DOI: 10.1307/mmj/2021708913
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引用次数: 0
Strongly Invertible Knots, Invariant Surfaces, and the Atiyah–Singer Signature Theorem 强可逆结、不变量曲面和Atiyah-Singer签名定理
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-09-21 DOI: 10.1307/mmj/20226183
Antonio Alfieri, Keegan Boyle
{"title":"Strongly Invertible Knots, Invariant Surfaces, and the Atiyah–Singer Signature Theorem","authors":"Antonio Alfieri, Keegan Boyle","doi":"10.1307/mmj/20226183","DOIUrl":"https://doi.org/10.1307/mmj/20226183","url":null,"abstract":"We use the G-signature theorem to define an invariant of strongly invertible knots analogous to the knot signature.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86121659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
An Intrinsic Characterization of Bruhat–Tits Buildings Inside Analytic Groups 分析群内Bruhat-Tits结构的内在表征
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-09-13 DOI: 10.1307/mmj/20217220
Bertrand R'emy, Amaury Thuillier, A. Werner
{"title":"An Intrinsic Characterization of Bruhat–Tits Buildings Inside Analytic Groups","authors":"Bertrand R'emy, Amaury Thuillier, A. Werner","doi":"10.1307/mmj/20217220","DOIUrl":"https://doi.org/10.1307/mmj/20217220","url":null,"abstract":"Given a semisimple group over a complete non-Archimedean field, it is well known that techniques from non-Archimedean analytic geometry provide an embedding of the corresponding Bruhat-Tits builidng into the analytic space associated to the group; by composing the embedding with maps to suitable analytic proper spaces, this eventually leads to various compactifications of the building. In the present paper, we give an intrinsic characterization of this embedding.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81165073","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Local-Global Principles for Constant Reductive Groups over Semi-Global Fields 半全局域上常约化群的局部-全局原理
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-08-27 DOI: 10.1307/mmj/20217219
J.-L. Colliot-Th'elene, D. Harbater, Julia Hartmann, D. Krashen, R. Parimala, V. Suresh
{"title":"Local-Global Principles for Constant Reductive Groups over Semi-Global Fields","authors":"J.-L. Colliot-Th'elene, D. Harbater, Julia Hartmann, D. Krashen, R. Parimala, V. Suresh","doi":"10.1307/mmj/20217219","DOIUrl":"https://doi.org/10.1307/mmj/20217219","url":null,"abstract":"We study local-global principles for torsors under reductive linear algebraic groups over semi-global fields; i.e., over one variable function fields over complete discretely valued fields. We provide conditions on the group and the semiglobal field under which the local-global principle holds, and we compute the obstruction to the local-global principle in certain classes of examples. Using our description of the obstruction, we give the first example of a semisimple simply connected group over a semi-global field where the local-global principle fails. Our methods include patching and R-equivalence.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74879133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
The Integer Group Determinants for the Heisenberg Group of Order p3 p3阶Heisenberg群的整数群行列式
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-08-10 DOI: 10.1307/mmj/20216124
Michael J. Mossinghoff, Christopher G. Pinner
{"title":"The Integer Group Determinants for the Heisenberg Group of Order p3","authors":"Michael J. Mossinghoff, Christopher G. Pinner","doi":"10.1307/mmj/20216124","DOIUrl":"https://doi.org/10.1307/mmj/20216124","url":null,"abstract":"We establish a congruence satisfied by the integer group determinants for the non-abelian Heisenberg group of order $p^3$. We characterize all determinant values coprime to $p$, give sharp divisibility conditions for multiples of $p$, and determine all values when $p=3$. We also provide new sharp conditions on the power of $p$ dividing the group determinants for $mathbb Z_p^2$. For a finite group, the integer group determinants can be understood as corresponding to Lind's generalization of the Mahler measure. We speculate on the Lind-Mahler measure for the discrete Heisenberg group and for two other infinite non-abelian groups arising from symmetries of the plane and 3-space.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83034165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Profinite Rigidity, Kleinian Groups, and the Cofinite Hopf Property 极限刚性、Kleinian群和有限Hopf性质
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-07-30 DOI: 10.1307/mmj/20217218
M. Bridson, A. Reid
{"title":"Profinite Rigidity, Kleinian Groups, and the Cofinite Hopf Property","authors":"M. Bridson, A. Reid","doi":"10.1307/mmj/20217218","DOIUrl":"https://doi.org/10.1307/mmj/20217218","url":null,"abstract":"Let Γ be a non-elementary Kleinian group and H < Γ a finitely generated, proper subgroup. We prove that if Γ has finite co-volume, then the profinite completions of H and Γ are not isomorphic. If H has finite index in Γ, then there is a finite group onto which H maps but Γ does not. These results streamline the existing proofs that there exist full-sized groups that are profinitely rigid in the absolute sense. They build on a circle of ideas that can be used to distinguish among the profinite completions of subgroups of finite index in other contexts, e.g. limit groups. We construct new examples of profinitely rigid groups, including the fundamental group of the hyperbolic 3-manifold Vol(3) and of the 4-fold cyclic branched cover of the figure-eight knot. We also prove that if a lattice in PSL(2,C) is profinitely rigid, then so is its normalizer in PSL(2,C). Dedicated to Gopal Prasad on the occasion of his 75th birthday","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88773215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Bowditch Taut Spectrum and Dimensions of Groups Bowditch拉紧谱和群的维数
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-07-22 DOI: 10.1307/mmj/20216121
Eduardo Mart'inez-Pedroza, Luis Jorge S'anchez Saldana
{"title":"Bowditch Taut Spectrum and Dimensions of Groups","authors":"Eduardo Mart'inez-Pedroza, Luis Jorge S'anchez Saldana","doi":"10.1307/mmj/20216121","DOIUrl":"https://doi.org/10.1307/mmj/20216121","url":null,"abstract":"For a finitely generated group $G$, let $H(G)$ denote Bowditch's taut loop length spectrum. We prove that if $G=(Aast B) / langle!langle mathcal R rangle!rangle $ is a $C'(1/12)$ small cancellation quotient of a the free product of finitely generated groups, then $H(G)$ is equivalent to $H(A) cup H(B)$. We use this result together with bounds for cohomological and geometric dimensions, as well as Bowditch's construction of continuously many non-quasi-isometric $C'(1/6)$ small cancellation $2$-generated groups to obtain our main result: Let $mathcal{G}$ denote the class of finitely generated groups. The following subclasses contain continuously many one-ended non-quasi-isometric groups: $bulletleft{Gin mathcal{G} colon underline{mathrm{cd}}(G) = 2 text{ and } underline{mathrm{gd}}(G) = 3 right}$ $bulletleft{Gin mathcal{G} colon underline{underline{mathrm{cd}}}(G) = 2 text{ and } underline{underline{mathrm{gd}}}(G) = 3 right}$ $bulletleft{Gin mathcal{G} colon mathrm{cd}_{mathbb{Q}}(G)=2 text{ and } mathrm{cd}_{mathbb{Z}}(G)=3 right}$ On our way to proving the aforementioned results, we show that the classes defined above are closed under taking relatively finitely presented $C'(1/12)$ small cancellation quotients of free products, in particular, this produces new examples of groups exhibiting an Eilenberg-Ganea phenomenon for families. We also show that if there is a finitely presented counter-example to the Eilenberg-Ganea conjecture, then there are continuously many finitely generated one-ended non-quasi-isometric counter-examples.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91273930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Minkowski Equality of Big Divisors 大因数的闵可夫斯基等式
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-07-11 DOI: 10.1307/mmj/20216107
S. Cutkosky
{"title":"The Minkowski Equality of Big Divisors","authors":"S. Cutkosky","doi":"10.1307/mmj/20216107","DOIUrl":"https://doi.org/10.1307/mmj/20216107","url":null,"abstract":"We give conditions characterizing equality in the Minkowski inequality for big divisors on a projective variety. Our results draw on the extensive history of research on Minkowski inequalities in algebraic geometry.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74198108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The Topology of Projective Codes and the Distribution of Zeros of Odd Maps 投影码的拓扑与奇映射的零分布
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-06-28 DOI: 10.1307/mmj/20216170
Henry Adams, Johnathan Bush, F. Frick
{"title":"The Topology of Projective Codes and the Distribution of Zeros of Odd Maps","authors":"Henry Adams, Johnathan Bush, F. Frick","doi":"10.1307/mmj/20216170","DOIUrl":"https://doi.org/10.1307/mmj/20216170","url":null,"abstract":"We show that the size of codes in projective space controls structural results for zeros of odd maps from spheres to Euclidean space. In fact, this relation is given through the topology of the space of probability measures on the sphere whose supports have diameter bounded by some specific parameter. Our main result is a generalization of the Borsuk--Ulam theorem, and we derive four consequences of it: (i) We give a new proof of a result of Simonyi and Tardos on topological lower bounds for the circular chromatic number of a graph; (ii) we study generic embeddings of spheres into Euclidean space and show that projective codes give quantitative bounds for a measure of genericity of sphere embeddings; and we prove generalizations of (iii) the Ham Sandwich theorem and (iv) the Lyusternik--Shnirel'man--Borsuk covering theorem for the case where the number of measures or sets in a covering, respectively, may exceed the ambient dimension.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88789500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Do the Hodge Spectra Distinguish Orbifolds from Manifolds? Part 1 霍奇光谱能区分轨道和流形吗?第1部分
IF 0.9 3区 数学
Michigan Mathematical Journal Pub Date : 2021-06-15 DOI: 10.1307/mmj/20216126
Katie Gittins, Carolyn Gordon, Magda Khalile, I. M. Solis, Mary R. Sandoval, E. Stanhope
{"title":"Do the Hodge Spectra Distinguish Orbifolds from Manifolds? Part 1","authors":"Katie Gittins, Carolyn Gordon, Magda Khalile, I. M. Solis, Mary R. Sandoval, E. Stanhope","doi":"10.1307/mmj/20216126","DOIUrl":"https://doi.org/10.1307/mmj/20216126","url":null,"abstract":"We examine the relationship between the singular set of a compact Riemannian orbifold and the spectrum of the Hodge Laplacian on $p$-forms by computing the heat invariants associated to the $p$-spectrum. We show that the heat invariants of the $0$-spectrum together with those of the $1$-spectrum for the corresponding Hodge Laplacians are sufficient to distinguish orbifolds with singularities from manifolds as long as the singular sets have codimension $le 3.$ This is enough to distinguish orbifolds from manifolds for dimension $le 3.$","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77374887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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