# Topology Seminar

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Mon., Nov. 14, 2022 1:00 p.m.
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Location: Zoom
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**Speaker: **Sarah Petersen, MPIM Bonn

**Title: **The *RO*(*C*_{2})-graded homology of *C*_{2}-equivariant Eilenberg–MacLane spaces (512 kB)

**Abstract: **

This talk describes an extension of Ravenel–Wilson Hopf ring techniques to *C*_{2}-equivariant homotopy theory. Our main application and motivation for introducing these methods is a computation of the *RO*(*C*_{2})-graded homology of *C*_{2}-equivariant Eilenberg–MacLane spaces. The result we obtain for *C*_{2}-equivariant Eilenberg–MacLane spaces associated to the constant Mackey functor **F**_{2} gives a *C*_{2}-equivariant analogue of the classical computation due to Serre at the prime 2. We also investigate a twisted bar spectral sequence computing the homology of these equivariant Eilenberg–MacLane spaces.

**Zoom Link:** https://uregina-ca.zoom.us/j/99127226830?pwd=bnFQR1R3UUdyWUxqSS9JMExMRlZwZz09