Noncommutative differential calculus, homotopy BV algebras and formality conjectures

2000/02/15 by Dmitri Tamarkin, Tamarkin, Dmitri, Boris Tsygan +1 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Nonlinear Waves and Solitons #math.AG #math.KT

paper · pdf · doi:10.48550/arxiv.math/0002116

19 pages

arxiv created 2000/02/15 · openalex publication_date 2000/02/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a notion of astrongly homotopy BV algebra and apply it to deformation theory problems. Formality conjectures for Hochschild and cyclic chains are formulated. We prove some partial results supporting these conjectures.

Citations

• On the cyclic Formality conjecture
• Operads, homotopy algebra and iterated integrals for double loop spaces
• Three constructions of Frobenius manifolds: a comparative study
• Riemann-Roch theorems via deformation quantization
• Koszul duality for operads

Cited by

• A Computation of Tamarkin-Tsygan Calculus
• Takeuchi-Schneider equivalence and calculi for homogeneous spaces of Hopf algebroids

Related

• Formality of the homotopy calculus algebra of Hochschild (co)chains
• A formality framework for commutative deformations
• Deformations of algebras in noncommutative geometry
• Homotopy Batalin-Vilkovisky algebras
• Noncommutative deformation theory, the derived quotient, and DG singularity categories