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- L infty algebra
- DGA
- CY
- cobar construction
- L infty algebra
- dg manifold
- Calabi-Yau \(A_\infty{\hbox{-}}\)structures are studied in the context of open topological string theory.
\(A_\infty\) structures
Idea: associativity only up to higher coherent homotopy. Naturally present on the homology complex of any DGA.
Definitions: 
Examples:
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\(H_{\mathrm{dR}}({-})\)
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- \({\operatorname{HH}}({-})\)
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Any loop space.
Coherence
# A_infty algebra
Here
- First relation \(m_1^2=0\) makes \(A\) a chain complex
- Second relation makes multiplication a chain morphism
- Third relation makes \(m_2\) associative up to chain homotopy
- Higher relations impose homotopy coherence
See Gerstenhaber bracket, coalgebra, Maurer-Cartan equations. 
pre-CY structures
Somehow give rise to TQFTs. 
A_infty categories
Twisted complexes
# Bimodules
Related to tilting modulues 
