Cochain level May-Steenrod operations

DOI10.1515/forum-2020-0296zbMath1487.55026arXiv2010.02571OpenAlexW3206392516MaRDI QIDQ2121509

Anibal M. Medina-Mardones, Ralph M. Kaufmann

Publication date: 4 April 2022

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.02571

zbMATH Keywords

Steenrod operationsoperadssimplicial cochains$E_\infty$ operadcubical cochainsMay-Steenrod structure

Mathematics Subject Classification ID

Software, source code, etc. for problems pertaining to algebraic topology (55-04) Steenrod algebra (55S10) Chain complexes in algebraic topology (55U15) Abstract complexes in algebraic topology (55U05) Dyer-Lashof operations (55S12) Primary cohomology operations in algebraic topology (55S05) Symmetric products and cyclic products in algebraic topology (55S15)

Related Items (6)

A computer algebra system for the study of commutativity up to coherent homotopies ⋮ Pathlike co/bialgebras and their antipodes with applications to bi- and Hopf algebras appearing in topology, number theory and physics ⋮ Koszul Feynman categories ⋮ The diagonal of cellular spaces and effective algebro-homotopical constructions ⋮ New formulas for cup-\(i\) products and fast computation of Steenrod squares ⋮ Persistence Steenrod modules

Cites Work

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• Comprehensive factorisation systems
• The Steenrod algebra and its dual
• Dyer-Lashof-Cohen operations in Hochschild cohomology.
• Moduli space actions on the Hochschild co-chains of a Frobenius algebra. II: Correlators
• A Cartesian presentation of weak \(n\)-categories
• The homology of iterated loop spaces
• Monoidal globular categories as a natural environment for the theory of weak \(n\)-categories
• Iterated monoidal categories
• Arc operads and arc algebras
• Permutohedral structures on \(E_2\)-operads
• State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter
• Fermionic SPT phases in higher dimensions and bosonization
• Omega-categories and chain complexes
• Homotopy invariant algebraic structures on topological spaces
• A cochain level proof of Adem relations in the mod 2 Steenrod algebra
• A computer algebra system for the study of commutativity up to coherent homotopies
• An algebraic representation of globular sets
• An effective proof of the Cartan formula: the even prime
• Coverage in sensor networks via persistent homology
• Algebraic string operations
• The geometry of iterated loop spaces
• On the homology of non-connected monoids and their associated groups
• HPT and cocyclic operations
• Products of cocycles and extensions of mappings
• Computation of Cubical Steenrod Squares
• Operads and PROPs
• ON THE COBAR CONSTRUCTION
• Cohomology Operations (AM-50)
• String Topology: Background and Present State
• Dimension vs. genus: A surface realization of the little k-cubes and an E_∞operad
• Topology and data
• Geometry of loop spaces and the cobar construction
• Multivariable cochain operations and little 𝑛-cubes
• Combinatorial operad actions on cochains
• A finitely presented ${E}_{\infty}$-prop II: cellular context
• Feynman categories and representation theory
• E n -spectra and Dyer-Lashof operations
• A finitely presented ${E}_{\infty}$-prop I: algebraic context
• Topology of viral evolution
• Feynman Categories
• Configuration spaces and $\Theta _n$
• Adem-Cartan Operads
• Spin TQFTs and fermionic phases of matter
• Homology of Iterated Loop Spaces
• The Iteration of the Steenrod Squares in Algebraic Topology
• Homology Groups of Symmetric Groups and Reduced Power Operations
• Cyclic Reduced Powers of Cohomology Classes

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