Natural operations on the Hochschild complex of commutative Frobenius algebras via the complex of looped diagrams

Abstract

We define a dg-category of looped diagrams which we use to construct operations on the Hochschild complex of commutative Frobenius dg-algebras. We show that we recover the operations known for symmetric Frobenius dg-algebras constructed using Sullivan chord diagrams as well as all formal operations for commutative algebras (including Loday's lambda operations) and prove that there is a chain level version of a suspended Cactus operad inside the complex of looped diagrams. This recovers the suspended BV algebra structure on the Hochschild homology of commutative Frobenius algebras defined by Abbaspour and proves that it comes from an action on the Hochschild chains.

45 pages

References in corpus (2)

• Higher string topology operations
• On algebraic structures of the Hochschild complex

Cited by in corpus (5)

• String topology and configuration spaces of two points
• Singular Hochschild cohomology and algebraic string operations
• The complex of formal operations on the Hochschild chains of commutative algebras
• Comparing combinatorial models of moduli space and their compactifications
• On the homotopy type of the space of Sullivan diagrams