Hyperbolic manifolds without $\text{spin}^\mathbb{C}$ structures and non-vanishing higher order Stiefel-Whitney classes

Alan W. Reid; Connor Sell

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arXiv · 2302.08060

Hyperbolic manifolds without $\text{spin}^\mathbb{C}$ structures and non-vanishing higher order Stiefel-Whitney classes

Alan W. Reid·Connor Sell

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Abstract

We show that in every commensurability class of cusped arithmetic hyperbolic manifolds of simplest type of dimension $2n+2\geq 6$ there are manifolds $M$ such that the Stiefel-Whitney classes $w_{2j}(M)$ are non-vanishing for all $0 \leq 2j \leq n$. We also show that for the same commensurability classes there are manifolds (different from the previous ones) that do not admit a $\text{spin}^\mathbb{C}$ structure.

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BibTeX RIS

Alan W. Reid, Connor Sell. 2023-02-16. Hyperbolic manifolds without $\text{spin}^\mathbb{C}$ structures and non-vanishing higher order Stiefel-Whitney classes. https://arxiv.org/abs/2302.08060

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