Introduction to A-infinity algebras and modules

Abstract

These are expanded notes of four introductory talks on A-infinity algebras, their modules and their derived categories.

30 pages, expanded version, sketches of proofs added, references updated, final version to appear in Homology, Homotopy and Applications

References in corpus (2)

• Braid group actions on derived categories of coherent sheaves
• Bimodule complexes via strong homotopy actions

Cited by in corpus (29)

• D-branes, Categories and N=1 Supersymmetry
• Bordered Heegaard Floer homology: Invariance and pairing
• Obstructed D-Branes in Landau-Ginzburg Orbifolds
• LHC Signatures of Resonant CP Violation in a Minimal Supersymmetric Higgs Sector
• $A_{\infty }$-structures on an elliptic curve
• Three-dimensional topological field theory and symplectic algebraic geometry I
• Determinantal Barlow surfaces and phantom categories
• Generalized complexes and string field theory
• Derived categories of Burniat surfaces and exceptional collections
• Dehn twists and free subgroups of symplectic mapping class groups
• A-infinity structure and superpotentials
• Bimodules and branes in deformation quantization
• Lagrangian torus fibrations and homological mirror symmetry for the conifold
• The motivic Donaldson-Thomas invariants of (-2) curves
• Involutive A-infinity algebras and dihedral cohomology
• B-branes and supersymmetric quivers in 2d
• Deformation quantization with generators and relations
• Monopole Operators and Bulk-Boundary Relation in Holomorphic Topological Theories
• Invariance of orientation data for ind-constructible Calabi-Yau $A_{\infty }$ categories under derived equivalence
• Simplifying Weinstein Morse functions
• Homotopy Algebras in Higher Spin Theory
• Odd sphere bundles, symplectic manifolds, and their intersection theory
• A note on the Koszul complex in deformation quantization
• Khovanov homology detects split links
• Bar category of modules and homotopy adjunction for tensor functors
• A-infinity structure in string theory and the Yang-Mills equation
• Twisted Hodge diamonds give rise to non-Fourier-Mukai functors
• Gröbner Bases: Connecting Linear Algebra with Homological and Homotopical Algebra
• Formality of DG algebras (after Kaledin)