An isovariant Blakers--Massey theorem

2025/06/26 by Klang, Inbar, Yeakel, Sarah
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.21259

Abstract

An isovariant map is an equivariant map between G-spaces which strictly preserves isotropy groups. In this paper, we lay the groundwork for the study of isovariant stable homotopy theory. We prove an isovariant Blakers--Massey theorem and its n-cubical generalization, define a suitable notion of suspension (by a trivial representation sphere) in the isovariant category, and prove an isovariant Freudenthal suspension theorem.

Citations

• Isovariant homotopy theory and fixed point invariants
• The equivariant parametrized h-cobordism theorem, the non-manifold part
• An isovariant Elmendorf's theorem
• Parametrized spectra, a low-tech approach

Related

• An isovariant Elmendorf's theorem
• Isovariant homotopy theory and fixed point invariants
• The Picard group in equivariant homotopy theory via stable module categories
• Equivariant stable homotopy methods in the algebraic K-theory of infinite groups
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