Cartan calculus in string topology
Algebraic Topology
2023-05-03 v1 Geometric Topology
Abstract
In this manuscript, we investigate a Cartan calculus on the homology of free loop spaces which is introduced by Kuribayashi, Wakatsuki, Yamaguchi and the author. In particular, it is proved that the Cartan calculus can be described by the loop product and bracket in string topology. Moreover, by using the descriptions, we show that the loop product behaves well with respect to the Hodge decomposition of the homology of free loop spaces.
Cite
@article{arxiv.2305.01286,
title = {Cartan calculus in string topology},
author = {Takahito Naito},
journal= {arXiv preprint arXiv:2305.01286},
year = {2023}
}
Comments
11 pages