The twisted Cartesian model for the double path fibration

Details The twisted Cartesian model for the double path fibration The twisted Cartesian model for the double path fibration

2002-10-15

arxiv.org/abs/math/0210224v2

Mathematics

Algebraic Topology

37 pages, 8 figures, This final version (10-01-04) clarifies a number of issues in earlier version and includes computational

Scientific paper

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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