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.
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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.