A simplified summary of higher homotopy operations
Paper Title:
The algebra of higher homotopy operations
Published on:
22 July 2023
Primary Category:
Algebraic Topology
Paper Authors:
Samik Basu,
David Blanc,
Debasis Sen
Bullets
Key Details
Defines higher homotopy operations in a model-independent ∞-categorical framework
Shows values of operations can be combined under composition and addition
Provides explicit formulas for representing Whitehead products
Gives a 'higher Hilton decomposition' expressing operations in terms of Whitehead products
Studies higher order Whitehead products as an illustrative example
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A simplified summary of higher homotopy operations
This paper introduces a formalism for higher homotopy operations, which generalize Whitehead products to higher dimensions. It shows these operations interact in a coherent algebraic structure, allowing the expression of any homotopy class as a composite of fundamental classes and iterated higher operations. The approach uses simplicial methods and spectral sequences.
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