Thesis (Ph. D.)--University of Rochester. Department of Mathematics, 2019.
Bredon cohomology is a cohomology theory that applies to topological spaces
equipped with the group actions. The thesis is directed towards computation
of rational Bredon cohomology of equivariant polyhedral products and
equivariant configuration spaces in the case when the acting groups are small
non-abelian groups. A polyhedral product is a natural subspace of a Cartesian product, which
is specified by a simplicial complex K. The automorphism group Aut(K) of
K induces a group action on the polyhedral product. In the thesis we study
this group action and give a formula for the fixed point set of the polyhedral
product for any subgroup H of Aut(K). We use the fixed point data to
compute examples of Bredon cohomology. A configuration space of a topological space X refers to the topological
space of pairwise distinct points in X. For any group G, given a real linear
representation V , the configuration space of V has a natural diagonal G-
action. In the thesis we study this group action on the configuration space
and give a decomposition of the homology Bredon coefficient system of the configuration space and apply this to compute Bredon cohomology of the
configuration space.
