Massey products for homotopy inner products

2025/07/21 by Kate Poirier, Poirier, Kate, Thomas Tradler +3
Mathematics · #08A65 #46C99 (primary) #55S30 #57K99 (secondary) #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2507.15494

openalex publication_date 2025/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper defines Massey-type products for a homotopy inner product on an A_∞ algebra, called Massey inner products. We include an explicit description of ordinary Massey products for A_∞ algebras, and for A_∞ 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.

Citations

• An algebraic model for the constant loops map
• Formality is preserved under domination
• Higher order Massey products for algebras over algebraic operads
• On the behavior of Massey products under field extension
• Bigraded notions of formality and Aeppli-Bott-Chern-Massey products
• A compact non-formal closed G₂ manifold with b₁=1
• Infinity inner products on A-infinity algebras
• Configuration spaces are not homotopy invariant
• On non-formal simply connected manifolds

Related

• A_∞ structures and Massey products
• Higher order Massey products and applications
• Direct families of polytopes with nontrivial Massey products
• Non-trivial higher Massey products in moment-angle complexes
• Poincaré dualization and Massey products