The bitwisted Cartesian model for the free loop fibration |
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Authors: | Samson Saneblidze |
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Institution: | A. Razmadze Mathematical Institute, Department of Geometry and Topology, M. Alexidze st., 1, 0193 Tbilisi, Georgia |
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Abstract: | Using the notion of truncating twisting function from a simplicial set to a cubical set a special, bitwisted, Cartesian product of these sets is defined. For the universal truncating twisting function, the (co)chain complex of the corresponding bitwisted Cartesian product agrees with the standard Cartier (Hochschild) chain complex of the simplicial (co)chains. The modelling polytopes Fn are constructed. An explicit diagonal on Fn is defined and a multiplicative model for the free loop fibration ΩY→ΛY→Y is obtained. As an application we establish an algebra isomorphism H∗(ΛY;Z)≈S(U)⊗Λ(s−1U) for the polynomial cohomology algebra H∗(Y;Z)=S(U). |
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Keywords: | primary 55P35 55U05 52B05 05A18 05A19 secondary 55P10 |
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