The loop orbifold of the symmetric product

Details The loop orbifold of the symmetric product The loop orbifold of the symmetric product

2006-06-22

arxiv.org/abs/math/0606573v1

Mathematics

Algebraic Topology

12 pages

Scientific paper

By using the loop orbifold of the symmetric product, we give a formula for the Poincar\'e 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.

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