2014/02/26 by P. Christopher Staecker, Staecker, P. Christopher, Matthew L. Wright +1
Mathematics · #52B45 #55M20 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:52B45 #msc:55M20
paper · pdf · doi:10.48550/arxiv.1402.6391
11 pages, 3 figures
arxiv created 2014/02/26 · arxiv updated 2014/02/27
We define the notion of valuation on simplicial maps between geometric realizations of simplicial complexes in ℝn. 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 ℝn. Our definition not only provides a generalization of the Lefschetz number, but also yields a Hadwiger-style classification theorem for all such valuations.