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arXiv · 2412.00384

Quantitative Smoothing of Polyhedral Manifolds

Spencer Cattalani
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Abstract

We use a recent result of C. Lange to obtain a converse to a theorem of B. Bowditch in dimension at most $4$. In particular, we show that, for $n \leq 4$, a polyhedral $n$-manifold $X$ with bounded geometry is $K$-bi-Lipschitz homeomorphic to a Riemannian manifold $M$. We bound the constant $K$, the curvature, and the injectivity radius of $M$ by the bounds on the geometry of $X$.

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Spencer Cattalani. 2024-11-30. Quantitative Smoothing of Polyhedral Manifolds. https://arxiv.org/abs/2412.00384

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