2002/10/15 by Tornike Kadeishvili, Kadeishvili, Tornike, Samson Saneblidze +1
Mathematics · #05A18 #05A19 #52B05 #55P35 #55R05 #55U05 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:05A18 #msc:05A19 #msc:52B05 #msc:55P35 #msc:55R05 #msc:55U05
paper · pdf · doi:10.48550/arxiv.math/0210224
37 pages, 8 figures, This final version (10-01-04) clarifies a number of issues in earlier version and includes computational examples
arxiv created 2004/10/01 · arxiv updated 2009/11/30
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.