Introduces Goncharov Lie coalgebra from GL homology and uses it with spectral sequences to describe rational K-theory of fields via weight-3 polylogarithms beyond prior low-degree cases.
Operads, homotopy algebra and iterated integrals for double loop spaces
5 Pith papers cite this work. Polarity classification is still indexing.
5
Pith papers citing it
abstract
This paper provides some background to the theory of operads, used in the first author's papers on 2d topological field theory (hep-th/921204, CMP 159 (1994), 265-285; hep-th/9305013). It is intended for specialists.
verdicts
UNVERDICTED 5representative citing papers
Infinitely many manifold operads exist that are left or right bimodule cobordant to the Fulton-MacPherson operad yet not homotopy equivalent to it, via a surgery theory relying on tree combinatorics for operadic bimodules.
In monoidal abelian categories with enough right-flat projectives, the co-Hochschild complex of the unit's projective resolution carries a B_infinity-structure that is A_infinity-quasi-isomorphic to the derived endomorphism algebra of the unit and recovers the Hochschild complex for bimodules.
Defines operadic spectrum via Hochschild object plus residue, shows no functorial base change for classical spectra along monoidal functors, and builds a universal residue for a canonical functorial version.
Proposes a universal theory of spectral propagation in compositional operator networks governed by three invariants and proves theorems on decomposition, stability, and uniqueness of propagation rules.
citing papers explorer
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The Goncharov Lie coalgebra of a field
Introduces Goncharov Lie coalgebra from GL homology and uses it with spectral sequences to describe rational K-theory of fields via weight-3 polylogarithms beyond prior low-degree cases.
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Surgery on manifold operads
Infinitely many manifold operads exist that are left or right bimodule cobordant to the Fulton-MacPherson operad yet not homotopy equivalent to it, via a surgery theory relying on tree combinatorics for operadic bimodules.
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The $B_\infty$-structure on the derived endomorphism algebra of the unit in a monoidal category
In monoidal abelian categories with enough right-flat projectives, the co-Hochschild complex of the unit's projective resolution carries a B_infinity-structure that is A_infinity-quasi-isomorphic to the derived endomorphism algebra of the unit and recovers the Hochschild complex for bimodules.
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The Operadic Spectrum and Obstructions to Spectral Base Change
Defines operadic spectrum via Hochschild object plus residue, shows no functorial base change for classical spectra along monoidal functors, and builds a universal residue for a canonical functorial version.
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A Universal Theory of Spectral Propagation for Compositional Operator Networks
Proposes a universal theory of spectral propagation in compositional operator networks governed by three invariants and proves theorems on decomposition, stability, and uniqueness of propagation rules.