2002/11/14 by Yves Félix, Félix, Yves, Luc Menichi +3
Mathematics · #16E40 #17A30 #17B55 #55P35 #81T30 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #math.AT #math.GT #math.QA #msc:16E40 #msc:17A30 #msc:17B55 #msc:55P35 #msc:81T30
paper · pdf · doi:10.48550/arxiv.math/0211229
21 Pages
arxiv created 2002/11/14 · arxiv updated 2009/11/30
Let C be a differential graded coalgebra, ΩC the Adams cobar construction and C^\vee the dual algebra. We prove that for a large class of coalgebras C there is a natural isomorphism of Gerstenhaber algebras between the Hochschild cohomologies HH^∗ (C^\vee, C ^\vee) and HH^∗ (ΩC ; ΩC). This result permits to describe a Hodge decomposition of the loop space homology of a closed oriented manifold, in the sense of Chas-Sullivan, when the field of coefficients is of characteristic zero.