The loop orbifold of the symmetric product

• Autores: Ernesto Lupercio, Bernardo Uribe, Miguel A. Xicoténcatl
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 211, Nº 2, 2007, págs. 293-306
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2007.01.002
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• Resumen

  • 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 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 Poincaré duality in the case of the symmetric product orbifold, both ring structures are isomorphic.