Algebraic & Geometric Topology

Loop homology of some global quotient orbifolds

Yasuhiko Asao

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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 ( 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

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

Received: 8 June 2017
Revised: 11 July 2017
Accepted: 18 August 2017
First available in Project Euclid: 1 February 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55N45: Products and intersections 55N91: Equivariant homology and cohomology [See also 19L47] 55P35: Loop spaces 55P91: Equivariant homotopy theory [See also 19L47]

string topology free loop space homology orbifold


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.

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