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arXiv · 2510.23318

Semifree Isovariant Poincar\'e Spaces and the Gap Condition

Dominik Kirstein·Christian Kremer
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Abstract

We introduce the notion of a semifree isovariant $G$-Poincar\'e space, a homotopical notion interpolating between semifree closed smooth $G$-manifolds and the equivariant Poincar\'e spaces of [HKK24b]. It carries the additional structure of an equivariant Poincar\'e embedding of the fixed points of a semifree $G$-Poincar\'e space. Under suitable gap conditions on the codimension, we show that the space of isovariant structures on a semifree $G$-Poincar\'e space for a periodic finite group $G$ is highly connected, giving a useful construction tool for manifold structures on equivariant Poincar\'e spaces.

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Dominik Kirstein, Christian Kremer. 2025-10-27. Semifree Isovariant Poincar\'e Spaces and the Gap Condition. https://arxiv.org/abs/2510.23318

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