• Corpus ID: 31882807

A Hadwiger Theorem for Simplicial Maps

@article{Staecker2014AHT,
  title={A Hadwiger Theorem for Simplicial Maps},
  author={P. Christopher Staecker and Matthew L. Wright},
  journal={arXiv: Algebraic Topology},
  year={2014}
}
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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