Special Open Sets in Manifold Calculus

2013/05/27 by Daniel Pryor, Pryor, Daniel
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT

paper · pdf · doi:10.48550/arxiv.1305.6186

15 pages

arxiv created 2013/05/27 · arxiv updated 2013/05/28

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 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 O_k(M), the full subposet of 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 O_k(M) by more general subposets and see that we still recover the same notion of polynomial cofunctor.

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