Open Collections

Equivariant bordism and G-bundles

University of British Columbia

Let G be the cyclic group of 4 elements and H the subgroup of G of order 2. We study the actions of G on manifolds modulo the equivariant bordism relation by studying the equivariant bordism relation on G-vector bundles; specifically, we focus on G-vector bundles such that G action is free away from the zero section, and the isotropy group of each point in the base is equal to H. We obtain a complete set of characteristic numbers that deter mines when such a G-vector bundle is nulibordant. Using this result, we obtain a geometric splitting of the bordism classes of these bundles into ge ometrically simpler components. Furthermore, we determine a complete set of characteristic numbers for the bordism ring of G-manifolds. Finally, we generalize our results to a larger family of finite groups G.

Thesis/Dissertation

application/pdf

2009-04-27

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/7567

Mathematics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/