The twisted Cartesian model  for  the double path space fibration

Tornike Kadeishvili and Samson Saneblidze

 55R05, 55P35, 55U05, 52B05, 05A18, 05A19 

math.AT/0210224

A. Razmadze Mathematical Institute
Georgian Academy of Sciences
M. Aleksidze st., 1
380093 Tbilisi, Georgia

kade@rmi.acnet.ge



A. Razmadze Mathematical Institute
Georgian Academy of Sciences
M. Aleksidze st., 1
380093 Tbilisi, Georgia

sane@rmi.acnet.ge


The paper introduces the notion of a truncating twisting function
from a cubical set to a permutahedral set and the corresponding
notion of twisted Cartesian product of these sets. The latter
becomes a permutocubical set that models in particular the path
space 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.