Bordisms of manifolds with proper action of a discrete group: signatures and descriptions of $G$-bundles

Abstract

In this work the equivariant signature of a manifold with proper action of a discrete group is defined as an invariant of equivariant bordisms. It is shown that the computation of this signature can be reduced to its computation on fixed points sets equipped with their tubular neighborhoods. It is given a description of the equivariant vector bundles with action of a discrete group $G$ for the case when the action over the base is proper quasi-free, i.e. the stationary subgroup of any point is finite. The description is given in terms of some classifying space.

arXiv comment30 pages. arXiv admin note: text overlap with arXiv:0912.5047

References in corpus (2)

• Description of G-bundles over G-spaces with quasi-free proper action of discrete group II
• On a spectral sequence for equivariant K-theory

Cited by in corpus (1)

• Transverse noncommutative geometry of foliations