The loop orbifold of the symmetric product
Preprint
Abstract
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.Keywords
All Related Versions
This publication has 7 references indexed in Scilit:
- Orbifold string topologyGeometry & Topology, 2008
- Stringy K-theory and the Chern characterInventiones Mathematicae, 2006
- A localization principle for orbifold theories2006
- Orbifold Cohomology of the Symmetric ProductCommunications in Analysis and Geometry, 2005
- A New Cohomology Theory of OrbifoldCommunications in Mathematical Physics, 2004
- Orbifold cohomology for global quotientsDuke Mathematical Journal, 2003
- The Poincare Polynomial of a Symmetric ProductMathematical Proceedings of the Cambridge Philosophical Society, 1962