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.
Operads, homotopy algebra and iterated integrals for double loop spaces
3 Pith papers cite this work. Polarity classification is still indexing.
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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.
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UNVERDICTED 3representative citing papers
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.
citing papers explorer
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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.