Institute of Mathematics for Industry

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On loop homology twisted by a discrete torsion


Hold Date 2018-04-27 16:00~2018-04-27 17:00

Place Lecture Room S W1-C-514, West Zone 1, Ito campus, Kyushu University

Object person  

Speaker Yasuhiko ASAO (University of Tokyo)

Abstract:
As an extension of string topology due to Chas-Sullivan, Lupercio-Uribe-Xicot¥’{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 non-trivial loop products, and we can judge the non-triviality by a cohomology class of the finite group which acts on the manifold. The ring structure appearing threre is studied pure-algebraically as the “algebra of discrete torsion” by R. Kauffmann.