Pairs of pants, Pochhammer curves and $L^2$invariants
Abstract
We propose an intuitive interpretation for nontrivial $L^2$Betti numbers of compact Riemann surfaces in terms of certain loops in embedded pairs of pants. This description uses twisted homology associated to the Hurewicz map of the surface, and it satisfies a sewing property with respect to a large class of pairofpants decompositions. Applications to supersymmetric quantum mechanics incorporating AharonovBohm phases are briefly discussed, for both point particles and topological solitons (abelian and nonabelian vortices) in two dimensions.
 Publication:

arXiv eprints
 Pub Date:
 October 2014
 arXiv:
 arXiv:1410.2429
 Bibcode:
 2014arXiv1410.2429B
 Keywords:

 Mathematical Physics;
 Mathematics  Algebraic Topology;
 Mathematics  Geometric Topology
 EPrint:
 18 pages, 3 figures