105 research outputs found
A cubical model for a fibration
In the paper the notion of truncating twisting function from a
simplicial set to a cubical set and the corresponding notion of twisted
Cartesian product of these sets are introduced. The latter
becomes a cubical set whose chain complex coincides with the standard twisted
tensor product . This construction together with
the theory of twisted tensor products for homotopy G-algebras allows to obtain
multiplicative models for fibrations.Comment: 15 pages, 1 figur
Transferring homotopy commutative algebraic structures
We show that the sum over planar trees formula of Kontsevich and Soibelman
transfers C-infinity structures along a contraction. Applying this result to a
cosimplicial commutative algebra A^* over a field of characteristic zero, we
exhibit a canonical unital C-infinity structure on Tot(A^*), which is unital if
A^* is; in particular, we obtain a canonical C-infinity structure on the
cochain complex of a simplicial set.Comment: 14 page
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