A Hadwiger Theorem for Simplicial Maps

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.

arXiv comment11 pages, 3 figures

References in corpus (1)

• Axioms for the Lefschetz number as a lattice valuation

Cited by in corpus (1)

• Gauss-Bonnet for multi-linear valuations