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
2 Pith papers cite this work. Polarity classification is still indexing.
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2026 2verdicts
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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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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 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.