A classification of neighborhoods around leaves of a singular foliation
Simon-Raphael Fischer, Camille Laurent-Gengoux
TL;DR
This paper provides a classification framework for singular foliations based on the properties of a specific leaf and its transverse singular foliation, enhancing understanding of their local and global structures.
Contribution
It introduces a systematic classification method for singular foliations around a leaf with a specified transverse structure, filling a gap in foliation theory.
Findings
Classification criteria for singular foliations around leaves
Identification of invariants characterizing local foliation structures
Framework applicable to various types of singular foliations
Abstract
We classify singular foliations admitting a given leaf and a given transverse singular foliation.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Algebraic Geometry and Number Theory · Polynomial and algebraic computation