Factorization homology and calculus à la Kontsevich Soibelman

Abstract

Using factorization homology techniques, we give a simple proof of the action of Kontsevich and Soibelman operad on the pair consisting of Hochschild cohomology and Hochschild homology. The proof obviously extends to higher Hochschild cohomology and factorization (also called chiral) homology. Note that our result works in categories of chain complexes but also in categories of modules over a commutative ring spectrum.

28 pages

References in corpus (5)

• Dendroidal sets and simplicial operads
• From manifolds to invariants of E_n-algebras
• The Homotopy Theory of Simplicially Enriched Multicategories
• Structured singular manifolds and factorization homology
• Moduli spaces of algebras over non-symmetric operads

Cited by in corpus (7)

• The Hochschild Complex of a Finite Tensor Category
• Period mappings for noncommutative algebras
• Higher Hochschild cohomology of the Lubin-Tate ring spectrum
• $E_n$-cell attachments and a local-to-global principle for homological stability
• Some Higher Coalgebra
• Operads, modules and topological field theories
• A geometric approach to equivariant factorization homology and nonabelian Poincaré duality