Holonomy transformations for singular foliations

被引：16
|
作者：
Androulidakis, Iakovos [1 ]
Zambon, Marco [2 ,3 ]
机构：
[1] Univ Athens, Dept Math, GR-15784 Athens, Greece
[2] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain
[3] Univ Autonoma Madrid, ICMAT CSIC UAM UCM UC3M, E-28049 Madrid, Spain
来源：
ADVANCES IN MATHEMATICS | 2014年 / 256卷
关键词：
Singular foliation; Holonomy; Proper Lie groupoid; Linearization; Deformation; LIE ALGEBROIDS; VECTOR-FIELDS; THEOREM; LINEARIZATION; SMOOTHNESS; COHOMOLOGY; GROUPOIDS; MANIFOLDS; ORBITS;
D O I：
10.1016/j.aim.2014.02.003
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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. (c) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：348 / 397
页数：50
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