Local systems on the free loop space and finiteness of the Hofer-Zehnder capacity - Albers, Peter; Frauenfelder, Urs; Oancea, Alexandru (Mathematische Annalen, 2017)
In this article we examine under which conditions symplectic homology with local coefficients of a unit disk bundle D^*MD∗MD^*M vanishes. For instance this is the case if the Hurewicz map π _2(M)→ H_2(M;{\mathbb {Z}})π2(M)→H2(M;Z)π _2(M)→ H_2(M;{\mathbb {Z}}) is nonzero. As an application we prove finiteness of the π _1π1π _1-sensitive Hofer-Zehnder capacity of unit disk bundles in these cases. We also prove uniruledness for such cotangent bundles. Moreover, we find an obstruction to the existence of H-space structures on general topological spaces, formulated in terms of local systems.
Published online: 26 March 2016
Gesehen am 14.08.2017