On the length of cohomology spheres

Denise de Mattos; Edivaldo Lopes dos Santos; Nelson Silva

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arXiv · 2007.12788

On the length of cohomology spheres

Denise de Mattos·Edivaldo Lopes dos Santos·Nelson Silva

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Abstract

We present the length, a numerical cohomological index theory, of $ G $-spaces which are cohomology spheres and $ G $ is a $p$-torus or a torus group, where $p$ is a prime. As a consequence, we obtain Borsuk-Ulam and Bourgin-Yang type theorems in this context. A sharper version of the Bourgin-Yang theorem for topological manifolds is also proved. Also, we give some general results regarding the upper and lower bound for the length.

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Denise de Mattos, Edivaldo Lopes dos Santos, Nelson Silva. 2020-07-24. On the length of cohomology spheres. https://arxiv.org/abs/2007.12788

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