A \(C_2\)-equivariant analog of Mahowald’s Thom spectrum theorem. (English) Zbl 1409.55010
A classical theorem by M. Mahowald [Topology 16, 249–256 (1977; Zbl 0357.55020)] states that the Eilenberg-Mac Lane spectrum of \(\mathbb F_2\) can be obtained as the Thom spectrum of a certain double loop map \(\Omega^2 S^3 \to BO\). In the present paper, the authors prove a \(C_2\)-equivariant variant of this statement. They show that the Eilenberg-Mac Lane spectrum of the constant Mackey functor with value \(\mathbb F_2\) is equivalent as a \(C_2\)-spectrum to the Thom spectrum of a map \(\Omega^{\rho} S^{\rho + 1} \to B_{C_2}O\) where \(\rho\) is the regular representation. The strategy of proof is to compute that the map representing the Thom class induces an isomorphism in \(RO(C_2)\)-graded homology.
Reviewer: Steffen Sagave (Nijmegen)
MSC:
| 55P91 | Equivariant homotopy theory in algebraic topology |
| 55S91 | Equivariant operations and obstructions in algebraic topology |
Citations:
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