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arXiv · 2610.06747

The Euler characteristic of $Pin^{\pm}$ manifolds

Renee S. Hoekzema·Luuk Stehouwer·Simona Veselá
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Abstract

We completely determine the possible parities of the Euler characteristic of closed $Pin^{\pm}$-manifolds of a given dimension. As an application we partially calculate the controlled cut-and-paste groups $SKK_{2k+1}^{Pin^{\pm}}$, which were previously undetermined.

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Renee S. Hoekzema, Luuk Stehouwer, Simona Veselá. 2026-10-05. The Euler characteristic of $Pin^{\pm}$ manifolds. https://arxiv.org/abs/2610.06747

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