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Local systems on the free loop space and finiteness of the Hofer-Zehnder capacity | | Peter Albers
; Urs Frauenfelder
; Alexandru Oancea
; | | Date: |
8 Sep 2015 | | Abstract: | In this article we examine under which conditions symplectic homology with
local coefficients of a unit disk bundle $D^*M$ vanishes. For instance this is
the case if the Hurewicz map $pi_2(M) o H_2(M;mathbb{Z})$ is nonzero. As an
application we prove finiteness of the $pi_1$-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. | | Source: | arXiv, 1509.2455 | | Services: | Forum | Review | PDF | Favorites | |
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