scholarly journals Singular foliations of toric type

1999 ◽  
Vol 8 (1) ◽  
pp. 45-52
Author(s):  
Maria Isabel ◽  
Tavares Camacho ◽  
Felipe Cano
Keyword(s):  
Singular Foliations

scholarly journals Singularities of smooth mappings with patterns

2007 ◽  
Vol 137 (2) ◽  
pp. 415-430
Author(s):  
Kentaro Saji ◽  
Masatomo Takahashi
Keyword(s):  
Singularity Theory ◽  
Differential Topology ◽  
Local Classification ◽  
Singular Foliations

We study smooth mappings with patterns which given by certain divergence diagrams of smooth mappings. The divergent diagrams of smooth mappings can be regard as smooth mappings from manifolds with singular foliations. Our concerns are generic differential topology and generic smooth mappings with patterns. We give a generic semi-local classification of surfaces with singularities and patterns as an application of singularity theory.

On the geometry of singular foliations

2019 ◽  
Vol 2019 (4) ◽  
pp. 132-137
Author(s):  
O.Y. Qosimov
Keyword(s):  
Singular Foliations

scholarly journals Stefan–Sussmann singular foliations, singular subalgebroids and their associated sheaves

2016 ◽  
Vol 13 (Supp. 1) ◽  
pp. 1641001 ◽  
Author(s):  
Iakovos Androulidakis ◽  
Marco Zambon
Keyword(s):  
Compact Support ◽  
Tangent Bundle ◽  
Explicit Description ◽  
Lie Algebroid ◽  
Support Condition ◽  
Singular Foliation ◽  
Compactly Supported ◽  
Singular Foliations ◽  
Equivalent Characterization

We explain and motivate Stefan–Sussmann singular foliations, and by replacing the tangent bundle of a manifold with an arbitrary Lie algebroid, we introduce singular subalgebroids. Both notions are defined using compactly supported sections. The main results of this note are an equivalent characterization, in which the compact support condition is removed, and an explicit description of the sheaf associated to any Stefan–Sussmann singular foliation or singular subalgebroid.

scholarly journals TRANSVERSELY PROJECTIVE FOLIATIONS ON SURFACES: EXISTENCE OF MINIMAL FORM AND PRESCRIPTION OF MONODROMY

2007 ◽  
Vol 18 (06) ◽  
pp. 723-747 ◽  
Author(s):  
FRANK LORAY ◽  
JORGE VITÓRIO PEREIRA
Keyword(s):  
Ambient Space ◽  
Two Dimensional ◽  
Complex Manifolds ◽  
Projective Structures ◽  
Singular Foliations ◽  
Minimal Form ◽  
Natural Way ◽  
Projective Surfaces

We introduce a notion of minimal form for transversely projective structures of singular foliations on complex manifolds. Our first main result says that this minimal form exists and is unique when ambient space is two-dimensional. From this result, one obtains a natural way to produce invariants for transversely projective foliations on surfaces. Our second main result says that on projective surfaces one can construct singular transversely projective foliations with prescribed monodromy.

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