A Hadwiger Theorem for Simplicial Maps

P. Christopher Staecker; Matthew L. Wright

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arXiv · 1402.6391

A Hadwiger Theorem for Simplicial Maps

P. Christopher Staecker·Matthew L. Wright

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Abstract

We define the notion of valuation on simplicial maps between geometric realizations of simplicial complexes in $\mathbb{R}^n$. Valuations on simplicial maps are analogous to valuations on sets. In particular, we define the Lefschetz volumes, which are analogous to the intrinsic volumes of subsets of $\mathbb{R}^n$. Our definition not only provides a generalization of the Lefschetz number, but also yields a Hadwiger-style classification theorem for all such valuations.

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P. Christopher Staecker, Matthew L. Wright. 2014-02-26. A Hadwiger Theorem for Simplicial Maps. https://arxiv.org/abs/1402.6391

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