Loop homology of some global quotient orbifolds

Asao, Yasuhiko

doi:10.2140/agt.2018.18.613

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Loop homology of some global quotient orbifolds

Yasuhiko Asao

Algebraic & Geometric Topology 18 (2018) 613–633

DOI: 10.2140/agt.2018.18.613

Abstract

We determine the ring structure of the loop homology of some global quotient orbifolds. We can compute by our theorem the loop homology ring with suitable coefficients of the global quotient orbifolds of the form $[M ∕ G]$ for $M$ being some kinds of homogeneous manifolds, and $G$ being a finite subgroup of a path-connected topological group $G$ acting on $M$ . It is shown that these homology rings split into the tensor product of the loop homology ring $ℍ_{*} (L M)$ of the manifold $M$ and that of the classifying space of the finite group, which coincides with the center of the group ring $Z (k [G])$ .

Keywords

string topology, free loop space homology, orbifold

Mathematical Subject Classification 2010

Primary: 55N45, 55N91, 55P35, 55P91

References

Publication

Received: 8 June 2017

Revised: 11 July 2017

Accepted: 18 August 2017

Published: 10 January 2018

Authors

Yasuhiko Asao
Graduate School of Mathematical Sciences The University of Tokyo Tokyo Japan

Volume 18, issue 1 (2018)