The loop orbifold of the symmetric product

Lupercio, Ernesto; Uribe, Bernardo; Xicoténcatl, Miguel A.

The loop orbifold of the symmetric product

Authors

Lupercio, Ernesto

Uribe, Bernardo

Xicoténcatl, Miguel A.

Description

By using the loop orbifold of the symmetric product, we give a formula for the Poincaré polynomial of the free loop space of the Borel construction of the symmetric product. We also show that the Chas-Sullivan product structure in the homology of the free loop space of the Borel construction of the symmetric product induces a ring structure in the homology of the inertia orbifold of the symmetric product. This ring structure is compared to the one in cohomology defined through the usual field theory formalism as in the theory of Chen and Ruan.
12 pages