Strict hyperbolization preserves stable tangent bundles via new hyperbolizing pieces from hyperbolic cubulable groups, yielding infinitely many hyperbolic manifolds with all lower Stiefel-Whitney classes non-trivial and first orientable examples with non-trivial Pontryagin classes.
A cusped hyperbolic 4-manifold without spin structures
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abstract
We build a non-compact, orientable, hyperbolic four-manifold of finite volume that does not admit any spin structure.
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Stably tangential strict hyperbolization
Strict hyperbolization preserves stable tangent bundles via new hyperbolizing pieces from hyperbolic cubulable groups, yielding infinitely many hyperbolic manifolds with all lower Stiefel-Whitney classes non-trivial and first orientable examples with non-trivial Pontryagin classes.