The Burnside Ring and Equivariant Stable Cohomotopy for Infinite Groups
| dc.creator | Lueck, Wolfgang | |
| dc.date | 2005-04-04 | |
| dc.date | 2005-07-12 | |
| dc.date.accessioned | 2026-07-07T05:18:46Z | |
| dc.date.available | 2026-07-07T05:18:46Z | |
| dc.description | After we have given a survey on the Burnside ring of a finite group, we discuss and analyze various extensions of this notion to infinite (discrete) groups. The first three are the finite-G-set-version, the inverse-limit-version and the covariant Burnside group. The most sophisticated one is the fourth definition as the equivariant zero-th cohomotopy of the classifying space for proper actions. In order to make sense of this definition we define equivariant cohomotopy groups of finite proper equivariant CW-complexes in terms of maps between the sphere bundles associated to equivariant vector bundles. We show that this yields an equivariant cohomology theory with a multiplicative structure. We formulate a version of the Segal Conjecture for infinite groups. All this is analogous and related to the question what are the possible extensions of the notion of the representation ring of a finite group to an infinite group. Here possible candidates are projective class groups, Swan groups and the equivariant topological K-theory of the classifying space for proper actions. | |
| dc.description | 63 pages Added the word Stable in the title. Corrected typos. Added remark at the end about the Segal Conjecture in the torsionfree case | |
| dc.identifier | https://arxiv.org/abs/math/0504051 | |
| dc.identifier | http://arxiv.org/abs/math/0504051 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74779 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55P91, 19A22 | |
| dc.title | The Burnside Ring and Equivariant Stable Cohomotopy for Infinite Groups | |
| dc.type | text |