The $RO(Π)$-graded cohomology of $BC_{2}O(1)$

Speaker: Elizabeth Tatum – University of Bonn

Abstract: In the $G$-equivariant setting, one typically uses $RO(G)$-graded cohomology theories. Costenoble-Waner have constructed an extension of this grading, the $RO(\Pi)$-grading, which allows classical results from nonequivariant topology, such as the Thom Isomorphism Theorem and Poincare duality, to be imported to the $G$-equivariant setting. I will discuss the computation of the cohomology of $BC_{2}O(1)$, the classifying space for real $C_{2}$-line bundles, in this extended grading. This is joint work with Agnès Beaudry, Chloe Lewis, Clover May, and Sabrina Pauli.