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Infinity-operadic foundations for embedding calculus
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DOI：10.1112/topo.70071.png)
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Abstract
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Motivated by applications to spaces of embeddings and automorphisms of manifolds, we consider a tower of -categories of truncated right modules over a unital -operad . We study monoidality and naturality properties of this tower, identify its layers, describe the difference between the towers as varies and generalise these results to the level of Morita -categories. Applied to the -framed -operad, this extends Goodwillie-Weiss' embedding calculus and its layer identification to the level of bordism categories. Applied to other variants of the -operad, it yields new versions of embedding calculus, such as one for topological embeddings - based on - or one similar to Boavida de Brito-Weiss' configuration categories - based on . In addition, we prove a delooping result in the context of embedding calculus, establish a convergence result for topological embedding calculus, improve upon the smooth convergence result of Goodwillie, Klein and Weiss and deduce an Alexander trick for homology 4-spheres.
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