Obstructions to commutativity in positive characteristic
Published on:
25 April 2024
Primary Category:
Algebraic Topology
Paper Authors:
Oisín Flynn-Connolly
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Key Details
Defines new cohomology operations called cotriple products that obstruct commutativity
Computes secondary operations for strictly commutative algebras
Constructs counterexamples to characteristic 0 behavior
Defines higher cotriple products and studies their behavior
Proves rectification theorem: E-infinity algebras can be rectified if higher Steenrod operations vanish coherently
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Obstructions to commutativity in positive characteristic
This paper explores the relationship between commutative algebras and E-infinity algebras in positive characteristic. It defines new cohomology operations called cotriple products that generalize Massey products and serve as obstructions to commutativity. The paper computes secondary operations for strictly commutative algebras, constructs counterexamples, defines higher cotriple products, and proves that E-infinity algebras can be rectified if and only if higher Steenrod operations vanish coherently.
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