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

Alan W. Reid, Connor Sell

We show that in every commensurability class of cusped arithmetic hyperbolic manifolds of simplest type of dimension $2n+2\ge 6$ there are manifolds $M$ such that the Stiefel-Whit…