2004/12/23 by Cenap Özel, cenap ozel, ozel, cenap
Mathematics · Medicine · #55 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #math.AT #msc:55
paper · pdf · doi:10.48550/arxiv.math/0412476
9 pages
arxiv created 2004/12/23 · openalex publication_date 2004/12/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In \citebaker-ozel, by using Fredholm index we developed a version of Quillen's geometric cobordism theory for infinite dimensional Hilbert manifolds. This cobordism theory has a graded group structure under topological union operation and has push-forward maps for complex orientable Fredholm maps. In \citecenap-isr, by using Quinn's Transversality Theorem \citeQuinn, it has been shown that this cobordism theory has a graded ring structure under transversal intersection operation and has pull-back maps for smooth maps. It has been shown that the Thom isomorphism in this theory was satisfied for finite dimensional vector bundles over separable Hilbert manifolds and the projection formula for Gysin maps has been proved. In \citechas, Chas and Sullivan described an intersection product on the homology of loop space LM. In \citecohen, R. Cohen and J. Jones described a realization of the Chas-Sullivan loop product in terms of a ring spectrum structure on the Thom spectrum of a certain virtual bundle over the loop space. In this paper, we will extend this product on cobordism and bordism theories.