English

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

Quantum Algebra 2007-05-23 v4 Algebraic Topology Geometric Topology

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.

Keywords

Cite

@article{arxiv.math/0308005,
  title  = {On Spineless Cacti, Deligne's Conjecture and Connes--Kreimer's Hopf Algebra},
  author = {Ralph M. Kaufmann},
  journal= {arXiv preprint arXiv:math/0308005},
  year   = {2007}
}

Comments

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