The loop homology algebra of discrete torsion
Event details
Date | 25.09.2018 |
Hour | 10:15 › 11:15 |
Speaker | Yasuhiko Asao |
Location | |
Category | Conferences - Seminars |
Let $M$ be a closed oriented manifold with a finite group action by $G$.
We denote its Borel construction by $M_{G}$. As an extension of string
topology due to Chas-Sullivan, Lupercio-Uribe-Xicot$\’{e}$ncatl
constructed a graded commutative associative product (loop product) on $
H_{*}(LM_{G})$, which plays a significant role in the “orbifold string
topology” . They also showed that the constructed loop product is an
orbifold invariant. In this talk, we describe the orbifold loop product
by determining its "twisting" out of the ordinary loop product in term
of the group cohomology of $G$, when the action is homotopically trivial.
Through this description, the orbifold loop homology algebra can be
seen as R. Kauffmann's “algebra of discrete torsion”, which is a group
quotient object of Frobenius algebra. As a cororally, we see that the
orbifold loop product is a non-trivial orbifold invariant.
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