scholarly journals Classification of overtwisted contact structures on 3-manifolds

1989 ◽  
Vol 98 (3) ◽  
pp. 623-637 ◽  
Author(s):  
Y. Eliashberg
Keyword(s):  
Contact Structures

scholarly journals Classification of tight contact structures on small Seifert 3–manifolds with $e_0\geq 0$

2005 ◽  
Vol 134 (3) ◽  
pp. 909-916 ◽  
Author(s):  
Paolo Ghiggini ◽  
Paolo Lisca ◽  
András I. Stipsicz
Keyword(s):  
Contact Structures ◽  
Tight Contact

A SELF-LINKING FORMULA FOR CURVES IN THE HEISENBERG SPACE

2002 ◽  
Vol 11 (07) ◽  
pp. 1077-1087
Author(s):  
MARCOS M. DINIZ
Keyword(s):  
Dna Structure ◽  
Contact Structures ◽  
Contact Manifolds ◽  
Linking Number ◽  
Legendrian Curves

The formula Lk = Wr + Tw, which expresses the linking number of two curves that bound a ribbon as a sum of two terms, has particularly interested biologists and was used to understand the DNA structure. The study of Legendrian curves in contact manifolds, and in particular in the Heisenberg space, is attached to some important problems in geometry, as the problem of classification of contact structures. In this work, we show the analogue formula for curves in the Heisenberg space, we relate the writhing number with the Thurston-Benequin invariant of a Legendrian curve and derive some results directly from this formula.

scholarly journals On the classification of tight contact structures I

2000 ◽  
Vol 4 (1) ◽  
pp. 309-368 ◽  
Author(s):  
Ko Honda
Keyword(s):  
Contact Structures ◽  
Tight Contact

scholarly journals Existence and classification of overtwisted contact structures in all dimensions

2015 ◽  
Vol 215 (2) ◽  
pp. 281-361 ◽  
Author(s):  
Matthew Strom Borman ◽  
Yakov Eliashberg ◽  
Emmy Murphy
Keyword(s):  
Contact Structures

scholarly journals Classification of tight contact structures on surgeries on the figure-eight knot

2020 ◽  
Vol 24 (3) ◽  
pp. 1457-1517
Author(s):  
James Conway ◽  
Hyunki Min
Keyword(s):  
Contact Structures ◽  
Tight Contact ◽  
Figure Eight Knot

scholarly journals Classification of contact structures associated with the CR-structure of the complex indicatrix

2017 ◽  
Vol 25 (1) ◽  
pp. 163-176
Author(s):  
Elena Popovici
Keyword(s):  
Fixed Point ◽  
Tangent Bundle ◽  
Contact Structure ◽  
Contact Structures ◽  
Cr Structure ◽  
Almost Contact Metric ◽  
Metric Structures ◽  
Pseudo Convex ◽  
Almost Contact Metric Structures

Abstract By regarding the complex indicatrix as an embedded CR-hypersurface of the holomorphic tangent bundle in a fixed point, we analyze some aspects of the relations between its CR structure and the considered contact structure. Moreover, using the classification of the almost contact metric structures associated with a strongly pseudo-convex CR-structure, of D. Chinea and C. Gonzales, we determine the classes corresponding to the natural contact structure of the complex indicatrix and the new structures obtained under a gauge transformation.

On the classification of certain planar contact structures

2011 ◽  
Vol 134 (4) ◽  
pp. 529-542 ◽  
Author(s):  
M. Firat Arikan ◽  
Selahi Durusoy
Keyword(s):  
Contact Structures ◽  
Planar Contact

scholarly journals On Subcritically Stein Fillable 5-manifolds

2018 ◽  
Vol 61 (1) ◽  
pp. 85-96 ◽  
Author(s):  
Fan Ding ◽  
Hansjörg Geiges ◽  
Guangjian Zhang
Keyword(s):  
Fundamental Group ◽  
Contact Structure ◽  
Contact Structures ◽  
Homotopy Classification ◽  
Contact Manifolds ◽  
Almost Contact Structure ◽  
Diffeomorphism Type ◽  
Standard Contact ◽  
Simply Connected

AbstractWe make some elementary observations concerning subcritically Stein fillable contact structures on 5-manifolds. Specifically, we determine the diffeomorphism type of such contact manifolds in the case where the fundamental group is finite cyclic, and we show that on the 5-sphere, the standard contact structure is the unique subcritically ?llable one. More generally, it is shown that subcritically fillable contact structures on simply connected 5-manifolds are determined by their underlying almost contact structure. Along the way, we discuss the homotopy classification of almost contact structures.

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