On spineless cacti, Deligne's conjecture and Connes-Kreimer's Hopf algebra

By R. Kaufmann. 2003

65 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/246e338209aa98fcc87cfea6a2c12c14a28dfef2

Citations in the corpus

• On the cyclic Deligne conjecture (2004, unknown): “Q A ] 2 7 O ct 2 00 4”
• Hochschild homology of structured algebras (2011, unknown): “1] or [28] in the “spineless” version (corresponding to not having start halfedges at the white vertices in our language), and [63] with the spines, both in terms of bipartite black and white trees, which give a slightly different description of the same chain complex.”
• Algebraic String Operations (2006, unknown): “perad acts on the Hochschild cochain complex of an associative algebra. In the more general case of A∞-algebras, this conjecture was proved in [KoSo]. The original associative case was also proved in [Kau], [MS1], [Ta1], [Ta2], [V]. The discovery of String Topology [CS1] suggested that in the presen”