vix.ing · top · new · best · stats · spec

Euler calculus on spaces homeomorphic to definable sets and some applications

2018/06/29 by Macías-Virgós, E., Mosquera-Lois, D.
#03C64 #28A25 #55R05 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.11502

Abstract

We show that integration with respect to the Euler-Poincaré characteristic can be extended from the setting of definable sets to the setting of topological spaces homeomorphic to definable sets. We use that extension to generalize a result regarding sensor networks due to Ghrist and Baryshnikov, in order to make it more flexible in applications. Finally, we obtain both an extension and a combinatorial proof of a classical result about the Euler-Poincaré characteristic of fiber bundles.

Related