English

Commutative cocycles and stable bundles over surfaces

Algebraic Topology 2019-06-04 v3

Abstract

Commutative K-theory, a cohomology theory built from spaces of commuting matrices, has been explored in recent work of Adem, G\'{o}mez, Gritschacher, Lind, and Tillman. In this article, we use unstable methods to construct explicit representatives for the real commutative K-theory classes on surfaces. These classes arise from commutative O(2)-valued cocycles, and are analyzed via the point-wise inversion operation on commutative cocycles.

Keywords

Cite

@article{arxiv.1807.03736,
  title  = {Commutative cocycles and stable bundles over surfaces},
  author = {Daniel A. Ramras and Bernardo Villarreal},
  journal= {arXiv preprint arXiv:1807.03736},
  year   = {2019}
}

Comments

26 pages. Minor revisions. This version has been accepted for publication in Forum Math

R2 v1 2026-06-23T02:56:39.153Z