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SUMMARY:The loop homology algebra of discrete torsion
DTSTART:20180925T101500
DTEND:20180925T111500
DTSTAMP:20260916T224257Z
UID:f16fef0b1e47a096d94dfa5aea768fa7c9d9409bbbd3795a00968c9c
CATEGORIES:Conferences - Seminars
DESCRIPTION:Yasuhiko Asao\nLet $M$ be a closed oriented manifold with a fi
 nite group action by $G$. \nWe denote its Borel construction by $M_{G}$. 
 As an extension of string \ntopology due to Chas-Sullivan\, Lupercio-Urib
 e-Xicot$\\’{e}$ncatl \nconstructed a graded commutative associative pro
 duct (loop product) on $\nH_{*}(LM_{G})$\, which plays a significant role 
 in the “orbifold string \ntopology” . They also showed that the const
 ructed loop product is an \norbifold invariant. In this talk\, we describ
 e the orbifold loop product \nby determining its "twisting" out of  the 
 ordinary loop product in term \nof the group cohomology of $G$\, when the
  action is homotopically trivial.\n Through this description\, the orbifo
 ld loop homology algebra can be \nseen as R. Kauffmann's “algebra of di
 screte torsion”\, which is a group \nquotient object of Frobenius algeb
 ra. As a cororally\, we see that the \norbifold loop product is a non-tri
 vial orbifold invariant.
LOCATION:CM 0 12 https://plan.epfl.ch/?room=CM012
STATUS:CONFIRMED
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