Differential graded algebras, Steenrod cup-one products, binomial operations, and Massey products

Porter, Richard D.; Suciu, Alexander I.

doi:10.1016/j.topol.2021.107987

Cited by 2 publications

(6 citation statements)

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“…In subsequent work [27], we develop a theory within which generalized Massey triple and higher order products lead to invariants of 1-equivalence for dgas, and apply this to homotopy classification problems for spaces. Example 9.12 illustrates a particular instance of this approach.…”

Section: Massey Productsmentioning

confidence: 99%

“…We start with Massey triple products of the form u, u, u . We will develop this idea, in a more general context, in [27].…”

Section: Free Cup-one Algebrasmentioning

confidence: 99%

“…The next lemma computes the indeterminacy of these restricted Massey triple products. We sketch a proof here in the case A is the cochain algebra of a ∆-complex, and will give full details (in full generality) in [27].…”

Section: For An Elementmentioning

confidence: 99%

“…This structure allows us to define the free binomial cup-one differential graded algebra generated by a set, which will be developed in [26] into a theory of 1-minimal models over the integers and over Z p . This framework also provides the context for defining restricted triple Massey products, which is a particular case of a more general construction that will be developed in [27].…”

mentioning

confidence: 99%

“…We conclude with a construction of a family of spaces whose homotopy types cannot be distinguished by the usual cup products and triple Massey products, yet can be distinguished using our restricted Massey products. The theory of generalized Massey products continues the program initiated in [25] and is developed more fully in [27], along with further applications.…”

mentioning

confidence: 99%

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Differential graded algebras, Steenrod cup-one products, binomial operations, and Massey products

Porter,

Suciu

2021

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Motivated by the construction of Steenrod cup-i 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.

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Section: Massey Productsmentioning

confidence: 99%

“…We start with Massey triple products of the form u, u, u . We will develop this idea, in a more general context, in [27].…”

Section: Free Cup-one Algebrasmentioning

confidence: 99%

Section: For An Elementmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%