The loop orbifold of the symmetric product

[摘要] Using the loop orbifold of the symmetric product, we give a formula for the Poincare polynomial of the free loop space of the Borel construction of the symmetric product. We also show that the Chas-Sullivan orbifold 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. For a general almost complex orbifold, we define a new ring structure on the cohomology of its inertia orbifold which we call the virtual intersection ring. Finally we show that under Poincare duality in the case of the symmetric product orbifold, both ring structures are isomorphic. (C) 2007 Elsevier B.V. All rights reserved.

[发布日期] 2007-11-01