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.
Lundell and Stephen Weingram.The topology of CW complexes
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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.