Kervaire semi-characteristics in KK-theory and an Atiyah type vanishing theorem
Differential Geometry
2025-01-16 v2 Algebraic Topology
K-Theory and Homology
Abstract
On (4n + 1)-dimensional (noncompact) manifolds admitting proper cocompact Lie group actions, we explore the analytic and topological sides of Kervaire semi-characteristics. The analytic side puts together two interpretations, one via assembly maps, and the other via dimensions of kernels. The topological side is ensured by the proper cocompact version of the Hodge theorem. The two sides coincide and admit an Atiyah type vanishing theorem.
Keywords
Cite
@article{arxiv.2410.00794,
title = {Kervaire semi-characteristics in KK-theory and an Atiyah type vanishing theorem},
author = {Hao Zhuang},
journal= {arXiv preprint arXiv:2410.00794},
year = {2025}
}
Comments
16 pages. Revising an example