Strong homotopy inner product of an A-infinity algebra

Details Strong homotopy inner product of an A-infinity algebra Strong homotopy inner product of an A-infinity algebra

2007-09-26

arxiv.org/abs/0709.4189v1

Mathematics

Algebraic Topology

25 pages

Scientific paper

We introduce a strong homotopy notion of a cyclic symmetric inner product of an A-infinity algebra and prove a characterization theorem in the formalism of the infinity inner products by Tradler. We also show that it is equivalent to the notion of a non-constant symplectic structure on the corresponding formal non-commutative supermanifold. We show that (open Gromov-Witten type) potential for a cyclic filtered A-infinity algebra is invariant under the cyclic filtered A-infinity homomorphism up to reparametrization, cyclization and a constant addition, generalizing the work of Kajiura.

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