14 citations · 36 across the 18 of their papers we have counts for
22 papers
On the bialgebra structure of the free loop homology
Samson Saneblidze
We introduce a commutative product of degree on the homology of an -dimensional special cubical set and lift it on the free loop homology for $…
Secondary cohomology operations and the loop space cohomology
Samson Saneblidze
Motivated by the loop space cohomology we construct the secondary operations on the cohomology to be a Hopf algebra for a simply connected space The loo…
On the -bialgebra structure of the rational homotopy groups
Samson Saneblidze
We introduce the notion of an -bialgebra structure on a vector space. We show that the rational homotopy groups admit such a structure fo…
Comparing Diagonals on the Associahedra
Samson Saneblidze, Ronald Umble
We prove that the formula for the diagonal approximation on J. Stasheff's -dimensional associahedron derived by the current authors in 2004 agrees with the "ma…
Framed Matrices and -Bialgebras
Samson Saneblidze, Ronald Umble
We complete the construction of the biassociahedra , construct the free matrad , realize as the cellular chains of and define…
A combinatorial model for the free loop fibration
Manuel Rivera, Samson Saneblidze
We introduce the abstract notion of a closed necklical set in order to describe a functorial combinatorial model of the free loop fibration over the…