## EVENT DETAILS AND ABSTRACT

**Topology Seminar**
**Title:** Equivariant fundamental classes in RO(C_{2})-graded cohomology

**Speaker:** Christy Hazel

**Speaker Info:** University of Oregon

**Brief Description:**

**Special Note**:

**Abstract:**

Let $C_2$ denote the cyclic group of order two. Given a manifold with a $C_2$-action, we can consider its equivariant Bredon $RO(C_2)$-graded cohomology. In this talk, I will give an overview of $RO(C_2)$-graded cohomology in constant $\mathbb{Z}/2$ coefficients, and then explain how a version of the Thom isomorphism theorem in this setting can be used to develop a theory of fundamental classes for equivariant submanifolds. I will then illustrate how these classes can be used to understand the cohomology of any $C_2$-surface in constant $\mathbb{Z/2}$ coefficients, including the ring structure.

**Date:** Monday, December 02, 2019

**Time:** 4:10pm

**Where:** Lunt 104

**Contact Person:** Eva Belmont

**Contact email:** ebelmont@northwestern.edu

**Contact Phone:** 847-467-1634

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