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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 ℍ∗(LM) 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
Asao, Yasuhiko 1
@article{10_2140_agt_2018_18_613,
author = {Asao, Yasuhiko},
title = {Loop homology of some global quotient orbifolds},
journal = {Algebraic and Geometric Topology},
pages = {613--633},
publisher = {mathdoc},
volume = {18},
number = {1},
year = {2018},
doi = {10.2140/agt.2018.18.613},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.613/}
}
TY - JOUR AU - Asao, Yasuhiko TI - Loop homology of some global quotient orbifolds JO - Algebraic and Geometric Topology PY - 2018 SP - 613 EP - 633 VL - 18 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.613/ DO - 10.2140/agt.2018.18.613 ID - 10_2140_agt_2018_18_613 ER -
Asao, Yasuhiko. Loop homology of some global quotient orbifolds. Algebraic and Geometric Topology, Tome 18 (2018) no. 1, pp. 613-633. doi: 10.2140/agt.2018.18.613
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