Holonomy transformations for singular foliations |
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| Authors: | Iakovos Androulidakis Marco Zambon |
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| Institution: | 1. National and Kapodistrian University of Athens, Department of Mathematics, Panepistimiopolis, GR-15784 Athens, Greece;2. Universidad Autónoma de Madrid, Departamento de Matemáticas and ICMAT(CSIC-UAM-UC3M-UCM), Campus de Cantoblanco, 28049 Madrid, Spain |
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| Abstract: | In order to understand the linearization problem around a leaf of a singular foliation, we extend the familiar holonomy map from the case of regular foliations to the case of singular foliations. To this aim we introduce the notion of holonomy transformation. Unlike the regular case, holonomy transformations cannot be attached to classes of paths in the foliation, but rather to elements of the holonomy groupoid of the singular foliation. |
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| Keywords: | primary 53C12 53C29 secondary 22A25 93B18 |
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