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The twisted Cartesian model for the double path fibration

Tornike Kadeishvili·Samson Saneblidze
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Abstract

In the paper the notion of truncating twisting function from a cubical set to a permutahedral set and the corresponding notion of twisted Cartesian product of these sets are introduced. The latter becomes a permutocubical set that models in particular the path fibration on a loop space. The chain complex of this twisted Cartesian product in fact is a comultiplicative twisted tensor product of cubical chains of base and permutahedral chains of fibre. This construction is formalized as a theory of twisted tensor products for Hirsch algebras.

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BibTeXRIS

Tornike Kadeishvili, Samson Saneblidze. 2004-10-01. The twisted Cartesian model for the double path fibration. https://arxiv.org/abs/math/0210224

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