Massey products for homotopy inner products

TL;DR

This paper introduces Massey inner products for homotopy inner products on $A__$ algebras, revealing richer algebraic structures and applications in topology beyond traditional Massey products.

Contribution

It defines Massey inner products, provides explicit descriptions for $A__$ algebras and modules, and demonstrates their applications in topology, showing they contain more information than ordinary Massey products.

Findings

Massey inner products have complex internal structures.

Applications to lens spaces, links, and low-dimensional manifolds.

Reveals additional topological information beyond traditional Massey products.

Abstract

This paper defines Massey-type products for a homotopy inner product on an $A_\infty$ algebra, called Massey inner products. We include an explicit description of ordinary Massey products for $A_\infty$ algebras, and for $A_\infty$ modules, and show that Massey product sets can have interesting internal structure. We give non-trivial applications from lens spaces, links, and low dimensional manifolds, showing Massey inner products contain information beyond ordinary Massey products.