Differential graded algebras, Steenrod cup-one products, binomial operations, and Massey products
Abstract
Motivated by the construction of Steenrod cup- products in the singular cochain algebra of a space and in the algebra of non-commutative differential forms, we define a category of binomial cup-one differential graded algebras over the integers and over prime fields of positive characteristic. The Steenrod and Hirsch identities bind the cup-product, the cup-one product, and the differential in a package that we further enhance with a binomial ring structure arising from a ring of integer-valued rational polynomials. This structure allows us to define the free binomial cup-one differential graded algebra generated by a set and derive its basic properties. It also provides the context for defining restricted triple Massey products, which have a smaller indeterminacy than the classical ones, and hence, give stronger homotopy type invariants.
Keywords
Cite
@article{arxiv.2105.10753,
title = {Differential graded algebras, Steenrod cup-one products, binomial operations, and Massey products},
author = {Richard D. Porter and Alexander I. Suciu},
journal= {arXiv preprint arXiv:2105.10753},
year = {2022}
}
Comments
45 pages; accepted for publication in Topology and its Applications