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arXiv · 2604.24301

Gyration Stability for Products

Sebastian Chenery
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Abstract

A gyration is an operation on Poincar\'{e} Duality complexes that arises from a certain surgery on the product of a given complex $N$ and a sphere, parametrised by a chosen twisting. Of particular recent interest is the notion of gyration stability; that is, $N$ is gyration stable when all of its gyrations have the same homotopy type, regardless of the twisting used. We prove that a product $N\times M$ of two Poincar\'{e} Duality complexes is gyration stable when one of the product terms is itself gyration stable, and provide some examples of interest.

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Sebastian Chenery. 2026-04-27. Gyration Stability for Products. https://arxiv.org/abs/2604.24301

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