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Annals of K-Theory最新文献

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The universal six-functor formalism 泛六函子形式
IF 0.6
Annals of K-Theory Pub Date : 2020-09-28 DOI: 10.2140/akt.2022.7.599
B. Drew, Martin Gallauer
{"title":"The universal six-functor formalism","authors":"B. Drew, Martin Gallauer","doi":"10.2140/akt.2022.7.599","DOIUrl":"https://doi.org/10.2140/akt.2022.7.599","url":null,"abstract":"We prove that Morel-Voevodsky's stable $mathbb{A}^1$-homotopy theory affords the universal six-functor formalism.","PeriodicalId":42182,"journal":{"name":"Annals of K-Theory","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45449640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
The relative L2 index theorem for Galoiscoverings Galoiscoverings的相对L2指数定理
IF 0.6
Annals of K-Theory Pub Date : 2020-09-21 DOI: 10.2140/akt.2021.6.503
M. Benameur
{"title":"The relative L2 index theorem for Galois\u0000coverings","authors":"M. Benameur","doi":"10.2140/akt.2021.6.503","DOIUrl":"https://doi.org/10.2140/akt.2021.6.503","url":null,"abstract":"Given a Galois covering of complete spin manifolds where the base metric has PSC near infinity, we prove that for small enough epsilon > 0, the epsilon spectral projection of the Dirac operator has finite trace in the Atiyah von Neumann algebra. This allows us to define the L2 index in the even case and we prove its compatibility with the Xie-Yu higher index. We also deduce L2 versions of the classical Gromov-Lawson relative index theorems. Finally, we briefly discuss some Gromov-Lawson L2 invariants.","PeriodicalId":42182,"journal":{"name":"Annals of K-Theory","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43490719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
K-theoretic torsion and the zetafunction K理论扭转与ζ函数
IF 0.6
Annals of K-Theory Pub Date : 2020-09-21 DOI: 10.2140/akt.2022.7.77
John R. Klein, Cary Malkiewich
{"title":"K-theoretic torsion and the zeta\u0000function","authors":"John R. Klein, Cary Malkiewich","doi":"10.2140/akt.2022.7.77","DOIUrl":"https://doi.org/10.2140/akt.2022.7.77","url":null,"abstract":"We generalize to higher algebraic $K$-theory an identity (originally due to Milnor) that relates the Reidemeister torsion of an infinite cyclic cover to its Lefschetz zeta function. Our identity involves a higher torsion invariant, the endomorphism torsion, of a parametrized family of endomorphisms as well as a higher zeta function of such a family. We also exhibit several examples of families of endomorphisms having non-trivial endomorphism torsion.","PeriodicalId":42182,"journal":{"name":"Annals of K-Theory","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49415401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The spectrum of equivariant Kasparov theory for cyclic groups of prime order 素数阶循环群的等变Kasparov理论的谱
IF 0.6
Annals of K-Theory Pub Date : 2020-09-11 DOI: 10.2140/akt.2021.6.547
Ivo Dell’Ambrogio, R. Meyer
{"title":"The spectrum of equivariant Kasparov theory for cyclic groups of prime order","authors":"Ivo Dell’Ambrogio, R. Meyer","doi":"10.2140/akt.2021.6.547","DOIUrl":"https://doi.org/10.2140/akt.2021.6.547","url":null,"abstract":"We compute the Balmer spectrum of the equivariant bootstrap category of separable $G$-C*-algebras when $G$ is a group of prime order.","PeriodicalId":42182,"journal":{"name":"Annals of K-Theory","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44655916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
An equivariant PPV theorem and Paschke–Higsonduality 一个等变PPV定理和paschke - higson对偶
IF 0.6
Annals of K-Theory Pub Date : 2020-01-27 DOI: 10.2140/akt.2022.7.237
M. Benameur, Indrava Roy
{"title":"An equivariant PPV theorem and Paschke–Higson\u0000duality","authors":"M. Benameur, Indrava Roy","doi":"10.2140/akt.2022.7.237","DOIUrl":"https://doi.org/10.2140/akt.2022.7.237","url":null,"abstract":"We prove an equivariant localized and norm-controlled version of the Pimsner-Popa-Voiculescu theorem. As an application, we deduce a proof of the Paschke-Higson duality for transformation groupoids.","PeriodicalId":42182,"journal":{"name":"Annals of K-Theory","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45472857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Positive scalar curvature and an equivariant Callias-type index theorem for proper actions 正标量曲率和固有作用的等变callias型指标定理
IF 0.6
Annals of K-Theory Pub Date : 2020-01-21 DOI: 10.2140/akt.2021.6.319
Haoyang Guo, P. Hochs, V. Mathai
{"title":"Positive scalar curvature and an equivariant Callias-type index theorem for proper actions","authors":"Haoyang Guo, P. Hochs, V. Mathai","doi":"10.2140/akt.2021.6.319","DOIUrl":"https://doi.org/10.2140/akt.2021.6.319","url":null,"abstract":"For a proper action by a locally compact group $G$ on a manifold $M$ with a $G$-equivariant Spin-structure, we obtain obstructions to the existence of complete $G$-invariant Riemannian metrics with uniformly positive scalar curvature. We focus on the case where $M/G$ is noncompact. The obstructions follow from a Callias-type index theorem, and relate to positive scalar curvature near hypersurfaces in $M$. We also deduce some other applications of this index theorem. If $G$ is a connected Lie group, then the obstructions to positive scalar curvature vanish under a mild assumption on the action. In that case, we generalise a construction by Lawson and Yau to obtain complete $G$-invariant Riemannian metrics with uniformly positive scalar curvature, under an equivariant bounded geometry assumption.","PeriodicalId":42182,"journal":{"name":"Annals of K-Theory","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47236204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
The plethory of operations in complextopological K-theory 复拓扑k理论中运算的完备论
IF 0.6
Annals of K-Theory Pub Date : 2020-01-06 DOI: 10.2140/akt.2021.6.481
William Mycroft, Sarah Whitehouse
{"title":"The plethory of operations in complex\u0000topological K-theory","authors":"William Mycroft, Sarah Whitehouse","doi":"10.2140/akt.2021.6.481","DOIUrl":"https://doi.org/10.2140/akt.2021.6.481","url":null,"abstract":"We provide a concrete introduction to the topologised, graded analogue of an algebraic structure known as a plethory, originally due to Tall and Wraith. Stacey and Whitehouse showed this structure is present on the cohomology operations for a suitable generalised cohomology theory. We compute an explicit expression for the plethory of operations for complex topological K-theory. This is formulated in terms of a plethory enhanced with structure corresponding to the looping of operations. In this context we show that the familiar lambda operations generate all the operations.","PeriodicalId":42182,"journal":{"name":"Annals of K-Theory","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41726061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Excision in equivariant fibred G-theory 等变纤维G-理论中的消去
IF 0.6
Annals of K-Theory Pub Date : 2019-11-21 DOI: 10.2140/akt.2020.5.721
G. Carlsson, B. Goldfarb
{"title":"Excision in equivariant fibred G-theory","authors":"G. Carlsson, B. Goldfarb","doi":"10.2140/akt.2020.5.721","DOIUrl":"https://doi.org/10.2140/akt.2020.5.721","url":null,"abstract":"This paper provides a generalization of excision theorems in controlled algebra in the context of equivariant G-theory with fibred control and families of bounded actions. It also states and proves several characteristic features of this theory such as existence of the fibred assembly and the fibrewise trivialization.","PeriodicalId":42182,"journal":{"name":"Annals of K-Theory","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42399597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On Fredholm boundary conditions on manifolds with corners, I: Global corner cycles obstructions 关于带角流形上的Fredholm边界条件，I：全局角循环障碍
IF 0.6
Annals of K-Theory Pub Date : 2019-10-24 DOI: 10.2140/akt.2021.6.607
P. C. Rouse, J. Lescure, Mario Velásquez
{"title":"On Fredholm boundary conditions on manifolds with corners, I: Global corner cycles obstructions","authors":"P. C. Rouse, J. Lescure, Mario Velásquez","doi":"10.2140/akt.2021.6.607","DOIUrl":"https://doi.org/10.2140/akt.2021.6.607","url":null,"abstract":"Given a connected manifold with corners of any codimension there is a very basic and computable homology theory called conormal homology defined in terms of faces and orientations of their conormal bundles, and whose cycles correspond geometrically to corner's cycles. \u0000Our main theorem is that, for any manifold with corners $X$ of any codimension, there is a natural and explicit morphism $$K_*(mathcal{K}_b(X)) stackrel{T}{longrightarrow} H^{pcn}_*(X,mathbb{Q})$$ between the $K-$theory group of the algebra $mathcal{K}_b(X)$ of $b$-compact operators for $X$ and the periodic conormal homology group with rational coeficients, and that $T$ is a rational isomorphism. \u0000As shown by the first two authors in a previous paper this computation implies that the rational groups $H^{pcn}_{ev}(X,mathbb{Q})$ provide an obstruction to the Fredholm perturbation property for compact connected manifold with corners. \u0000The difference with respect to the previous article of the first two authors in which they solve this problem for low codimensions is that we overcome in the present article the problem of computing the higher spectral sequence K-theory differentials associated to the canonical filtration by codimension by introducing an explicit topological space whose singular cohomology is canonically isomorphic to the conormal homology and whose K-theory is naturally isomorphic to the $K-$theory groups of the algebra $mathcal{K}_b(X)$.","PeriodicalId":42182,"journal":{"name":"Annals of K-Theory","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43306336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Relative K-theory via 0-cycles in finitecharacteristic 有限特性中通过0环的相对k理论
IF 0.6
Annals of K-Theory Pub Date : 2019-10-15 DOI: 10.2140/akt.2021.6.673
Rahul Gupta, A. Krishna
{"title":"Relative K-theory via 0-cycles in finite\u0000characteristic","authors":"Rahul Gupta, A. Krishna","doi":"10.2140/akt.2021.6.673","DOIUrl":"https://doi.org/10.2140/akt.2021.6.673","url":null,"abstract":"Let $R$ be a regular semi-local ring, essentially of finite type over a perfect field of characteristic $p ge 3$. We show that the cycle class map with modulus from an earlier work of the authors induces a pro-isomorphism between the additive higher Chow groups of relative 0-cycles and the relative $K$-theory of truncated polynomial rings over $R$. This settles the problem of equating 0-cycles with modulus and relative $K$-theory of such rings in all characteristics $neq 2$.","PeriodicalId":42182,"journal":{"name":"Annals of K-Theory","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45650515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
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