Infinity-Inner-Products on A-Infinity-Algebras

Abstract

In this paper the Hochschild-cochain-complex of an A-infinity-algebra A with values in an A-infinity-bimodule M over A and maps between them is defined. Then, an infinity-inner-product on A is defined to be an A-infinity-bimodule-map between A and its dual A*. There is a graph-complex associated to A-infinity-algebras with infinity-inner-product.

30 pages

References in corpus (3)

• Operads, homotopy algebra and iterated integrals for double loop spaces
• String Topology
• The BV Algebra on Hochschild Cohomology Induced by Infinity Inner Products

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• Bimodules and branes in deformation quantization
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• Picard-Lefschetz theory and dilating C^*-actions
• Invariance of orientation data for ind-constructible Calabi-Yau $A_{\infty }$ categories under derived equivalence
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• A-infinity-bimodules and Serre A-infinity-functors
• Fukaya categories of Lagrangian cobordisms and duality
• Strong homotopy inner product of an A-infinity algebra
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• On the obstructed Lagrangian Floer theory