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

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

2011-12-09

arxiv.org/abs/1112.2104v1

Mathematics

Algebraic Topology

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

Scientific paper

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.

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