Very good homogeneous functors in manifold calculus
| Autor: | Donald Stanley, Paul Arnaud Songhafouo Tsopméné |
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| Rok vydání: | 2019 |
| Předmět: |
Subcategory
Fundamental group Functor General Mathematics Zero object Vector bundle Mathematics::K-Theory and Homology Mathematics::Category Theory FOS: Mathematics Covariance and contravariance of vectors Calculus Algebraic Topology (math.AT) Mathematics - Algebraic Topology Abelian group Partially ordered set Mathematics |
| Zdroj: | Colloquium Mathematicum. 158:265-297 |
| ISSN: | 1730-6302 0010-1354 |
| Popis: | Let M be a smooth manifold, and let O(M) be the poset of open subsets of M. Let C be a category that has a zero object and all small limits. A homogeneous functor (in the sense of manifold calculus) of degree k from O(M) to C is called very good if it sends isotopy equivalences to isomorphisms. In this paper we show that the category VGHF of such functors is equivalent to the category of contravariant functors from the fundamental groupoid of Conf(k, M) to C, where Conf(k, M) stands for the unordered configuration space of k points in M. As a consequence of this result, we show that the category VGHF is equivalent to the category of representations of the fundamental group of Conf(k, M) in C, provided that Conf(k, M) is connected. We also introduce a subcategory of vector bundles that we call very good vector bundles, and we show that it is abelian, and equivalent to a certain category of very good functors. No change on the results. Added motivation to the introduction. The exposition has been improved and many straightforward proofs have been taken away. Now the new version is the half of the previous one |
| Databáze: | OpenAIRE |
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