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Embeddings from the point of view of immersion theory. I. (English) Zbl 0927.57027

Geom. Topol. 3, 67-101 (1999); erratum ibid. 15, No. 1, 407-409 (2011).
Let \(M\) and \(N\) be smooth manifolds without boundary. The author develops a suitable calculus of the cofunctors \(V \to \text{emb}(V,N)\) from the poset (category) of open subsets \(V\) of \(M\) to spaces. The work has been inspired by T. G. Goodwillie’s calculus of homotopy functors expounded in a series of papers [e.g., K-Theory 4, No. 1, 1-27 (1990; Zbl 0741.57021)], but it is not a special case. The study of such cofunctors are of potential importance to obtain an understanding of the space of smooth embeddings \(\text{emb}(M,N)\). As a main result, the author explicitly determines the terms in certain Taylor series for the cofunctors \(V \to \text{emb}(V,N)\).

MSC:

57R40 Embeddings in differential topology
57R42 Immersions in differential topology
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References:

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