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##### Department of Mathematics, University of California San Diego

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## The $RO(C_2)$-graded homology of $C_2$-equivariant Eilenberg-Maclane spaces

##### Abstract:

This talk describes work in progress computing the $H\underline{\mathbb{F}}_2$ homology of the $C_2$-equivariant Eilenberg-Maclane spaces associated to the constant Mackey functor $\underline{\mathbb{F}}_2$. We extend a Hopf ring argument of Ravenel-Wilson computing the mod p homology of non-equivariant Eilenberg-Maclane spaces to the $RO(C_2)$-graded setting. An important tool that arises in this equivariant context is the twisted bar spectral sequence which is quite complicated, lacking an explicit $E^2$ page and having arbitrarily long equivariant degree shifting differentials. We avoid working directly with these differentials and instead use a computational lemma of Behrens-Wilson along with norm and restriction maps to complete the computation.

Zhouli Xu