Geodesic
The H𝔽2–homology of C2–equivariant Eilenberg–Mac Lane spaces
Petersen, Sarah1
1 Department of Mathematics, University of Colorado Boulder, Boulder, CO, United States
Algebraic and Geometric Topology, Tome 24 (2024) no. 8, pp. 4487-4518

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2024.24.4487
Keywords: Equivariant homotopy theory, $RO(C_2)$–graded homology, $C_2$–equivariant Eilenberg–Mac Lane spaces, Hopf rings

Petersen, Sarah 1

1 Department of Mathematics, University of Colorado Boulder, Boulder, CO, United States 
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Petersen, Sarah. The H𝔽2–homology of C2–equivariant Eilenberg–Mac Lane spaces. Algebraic and Geometric Topology, Tome 24 (2024) no. 8, pp. 4487-4518. doi: 10.2140/agt.2024.24.4487

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