## Algebraic & Geometric Topology

### Loop homology of some global quotient orbifolds

Yasuhiko Asao

#### 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 $Z ( k [ G ] )$.

#### Article information

Source
Algebr. Geom. Topol., Volume 18, Number 1 (2018), 613-633.

Dates
Revised: 11 July 2017
Accepted: 18 August 2017
First available in Project Euclid: 1 February 2018

https://projecteuclid.org/euclid.agt/1517454228

Digital Object Identifier
doi:10.2140/agt.2018.18.613

Mathematical Reviews number (MathSciNet)
MR3748255

Zentralblatt MATH identifier
1385.55006

#### Citation

Asao, Yasuhiko. Loop homology of some global quotient orbifolds. Algebr. Geom. Topol. 18 (2018), no. 1, 613--633. doi:10.2140/agt.2018.18.613. https://projecteuclid.org/euclid.agt/1517454228

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