## EVENT DETAILS AND ABSTRACT

**Topology Seminar**
**Title:** A structure theorem for RO(G)-graded cohomology

**Speaker:** Clover May

**Speaker Info:** University of Oregon

**Brief Description:**

**Special Note**:

**Abstract:**

Computations of singular cohomology groups are very familiar. An equivariant analogue is RO(G)-graded Bredon cohomology with coefficients in a constant Mackey functor. Computations in this setting are often more challenging and are not well understood. In this
talk I will present a structure theorem for RO(C_2)-graded cohomology with \underline{Z/2} coefficients that substantially simplifies computations. The structure theorem says the cohomology of any finite C_2-CW complex decomposes as a direct sum of two basic pieces: shifted copies of the cohomology of a point and shifted copies of the cohomologies of spheres with the antipodal action. I will sketch the proof, which depends on a Toda bracket calculation, and give some examples.

**Date:** Monday, October 02, 2017

**Time:** 4:10pm

**Where:** Lunt 104

**Contact Person:** Prof. John Francis

**Contact email:** jnkf@math.northwestern.edu

**Contact Phone:** 847-491-5544

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