Abstract
Embedding Calculus, as described by Weiss, is a calculus of functors, suitable for studying contravariant functors from the poset of open subsets of a smooth manifold $M$, denoted $\mathcal{O}(M)$, to a category of topological spaces (of which the functor $Emb(-,N)$ for some fixed manifold $N$ is a prime example). Polynomial functors of degree $k$ can be characterized by their restriction to $\mathcal{O}_k(M)$, the full subposet of $\mathcal{O}(M)$ consisting of open sets which are a disjoint union of at most $k$ components, each diffeomorphic to the open unit ball. In this work, we replace $\mathcal{O}_k(M)$ by more general subposets and see that we still recover the same notion of polynomial cofunctor.
Citation
Daniel Pryor. "Special Open Sets in Manifold Calculus." Bull. Belg. Math. Soc. Simon Stevin 22 (1) 89 - 103, march 2015. https://doi.org/10.36045/bbms/1426856861
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