Abstract
Let and be smooth manifolds without boundary. Immersion theory suggests that an understanding of the space of smooth embeddings should come from an analysis of the cofunctor from the poset of open subsets of to spaces. We therefore abstract some of the properties of this cofunctor, and develop a suitable calculus of such cofunctors, Goodwillie style, with Taylor series and so on. The terms of the Taylor series for the cofunctor are explicitly determined. In a sequel to this paper, we introduce the concept of an analytic cofunctor from to spaces, and show that the Taylor series of an analytic cofunctor converges to . Deep excision theorems due to Goodwillie and Goodwillie–Klein imply that the cofunctor is analytic when .
Citation
Michael Weiss. "Embeddings from the point of view of immersion theory : Part I." Geom. Topol. 3 (1) 67 - 101, 1999. https://doi.org/10.2140/gt.1999.3.67
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