Seminar
On loop homology twisted by a discrete torsion

Hold Date 
20180427 16:00～20180427 17:00 


Place 
Lecture Room S W1C514, West Zone 1, Ito campus, Kyushu University 


Object person 



Speaker 
Yasuhiko ASAO (University of Tokyo) 

Abstract:
As an extension of string topology due to ChasSullivan, LupercioUribeXicot¥’{e}ncatl constructed a graded commutative associative product (loop product) on the homology of the free loop space of the Borel construction of oriented closed manifolds with finite group action, which plays a significant role in “orbifold string topology” . They also showed that the constructed loop product is an orbifold invariant. However, there are little examples of calculation for this ring structure, and it is impossible to distinguish the given orbifold from the trivial orbifold by the loop product computed so far. By restricting the situation to the case in which a finite group acts on a manifold homotopically trivially and enhancing insight, we achieve to compute the loop product for orbifolds in a wide class. Furthermore, there appears nontrivial loop products, and we can judge the nontriviality by a cohomology class of the finite group which acts on the manifold. The ring structure appearing threre is studied purealgebraically as the “algebra of discrete torsion” by R. Kauffmann.