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The $H \underline{\mathbb{F}}_2$–homology of $C_2$–equivariant Eilenberg–Mac Lane spaces

Sarah Petersen

Algebraic & Geometric Topology 24 (2024) 4487–4518
Abstract

We extend Ravenel–Wilson Hopf ring techniques to C2–equivariant homotopy theory. Our main application and motivation is a computation of the RO(C2)–graded homology of C2–equivariant Eilenberg–Mac Lane spaces. The result we obtain for C2–equivariant Eilenberg–Mac Lane spaces associated to the constant Mackey functor 𝔽¯2 gives a C2–equivariant analogue of the classical computation due to Serre. We also investigate a twisted bar spectral sequence computing the homology of these equivariant Eilenberg–Mac Lane spaces and suggest the existence of another twisted bar spectral sequence with E2–page given in terms of a twisted Tor functor.

Keywords
Equivariant homotopy theory, $RO(C_2)$–graded homology, $C_2$–equivariant Eilenberg–Mac Lane spaces, Hopf rings
Mathematical Subject Classification
Primary: 55P91
Secondary: 55N91, 55P20
References
Publication
Received: 12 July 2022
Revised: 18 January 2023
Accepted: 6 February 2023
Published: 17 December 2024
Authors
Sarah Petersen
Department of Mathematics
University of Colorado Boulder
Boulder, CO
United States

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