On Spineless Cacti, Deligne's Conjecture and Connes--Kreimer's Hopf Algebra

2003/08/01 by Ralph M. Kaufmann, Kaufmann, Ralph M.
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #math.AT #math.GT #math.QA

paper · pdf · doi:10.48550/arxiv.math/0308005

Version to appear in Topology. Some material rearranged, new appendix on the graph theoretical details for cacti. 69p. 5 figures elsart.cls

arxiv created 2006/10/25 · arxiv updated 2009/12/01

Abstract

Using a cell model for the little discs operad in terms of spineless cacti we give a minimal common topological operadic formalism for three a priori disparate algebraic structures: (1) a solution to Deligne's conjecture on the Hochschild complex, (2) the Hopf algebra of Connes and Kreimer, and (3) the string topology of Chas and Sullivan.

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