Commutative cocycles and stable bundles over surfaces

Commutative -theory, a cohomology theory built from spaces of commuting matrices, has been explored in recent work of Adem, Gómez, Gritschacher, Lind and Tillman. In this article, we use unstable methods to construct explicit representatives for the real commutative -theory classes on surfaces. Thes...

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Bibliographic Details
Published inForum mathematicum Vol. 31; no. 6; pp. 1395 - 1415
Main Authors Ramras, Daniel A., Villarreal, Bernardo
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 01.11.2019
Walter de Gruyter GmbH
Subjects
55N15
55R35
commuting matrices
Homology
vector bundle
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Summary:Commutative -theory, a cohomology theory built from spaces of commuting matrices, has been explored in recent work of Adem, Gómez, Gritschacher, Lind and Tillman. In this article, we use unstable methods to construct explicit representatives for the real commutative -theory classes on surfaces. These classes arise from commutative -valued cocycles and are analyzed via the point-wise inversion operation on commutative cocycles.
ISSN:0933-7741
1435-5337
DOI:10.1515/forum-2018-0163