scholarly journals Contact surgery and symplectic caps

2020 ◽  
Vol 52 (2) ◽  
pp. 379-394
Author(s):  
James Conway ◽  
John B. Etnyre
Keyword(s):  
Contact Surgery

scholarly journals Contact surgery and transverse invariants

2011 ◽  
Vol 4 (4) ◽  
pp. 817-834 ◽  
Author(s):  
Paolo Lisca ◽  
András I. Stipsicz
Keyword(s):  
Contact Surgery

scholarly journals On the contact Ozsváth-Szabó invariant

2010 ◽  
Vol 47 (1) ◽  
pp. 90-107
Author(s):  
Tolga Etgü ◽  
Burak Ozbagci
Keyword(s):  
Homology Group ◽  
Contact Structure ◽  
Floer Homology ◽  
Heegaard Floer Homology ◽  
Open Book ◽  
Open Book Decomposition ◽  
Heegaard Diagram ◽  
Contact Surgery ◽  
Heegaard Floer

Sarkar and Wang proved that the hat version of Heegaard Floer homology group of a closed oriented 3-manifold is combinatorial starting from an arbitrary nice Heegaard diagram and in fact every closed oriented 3-manifold admits such a Heegaard diagram. Plamenevskaya showed that the contact Ozsváth-Szabó invariant is combinatorial once we are given an open book decomposition compatible with a contact structure. The idea is to combine the algorithm of Sarkar and Wang with the recent description of the contact Ozsváth-Szabó invariant due to Honda, Kazez and Matić. Here we observe that the hat version of the Heegaard Floer homology group and the contact Ozsváth-Szabó invariant in this group can be combinatorially calculated starting from a contact surgery diagram. We give detailed examples pointing out to some shortcuts in the computations.

scholarly journals Handle moves in contact surgery diagrams

2009 ◽  
Vol 2 (1) ◽  
pp. 105-122 ◽  
Author(s):  
Fan Ding ◽  
Hansjörg Geiges
Keyword(s):  
Contact Surgery

scholarly journals A NOTE ON CONTACT SURGERY DIAGRAMS

2005 ◽  
Vol 16 (01) ◽  
pp. 87-99 ◽  
Author(s):  
BURAK OZBAGCI
Keyword(s):  
Positive Integer ◽  
Contact Structure ◽  
Overtwisted Contact Structure ◽  
Contact Surgery

We prove that for any positive integer k, the stabilization of a [Formula: see text]-surgery curve in a contact surgery diagram induces an overtwisted contact structure.

scholarly journals The diffeotopy group of S1×S2 via contact topology

2010 ◽  
Vol 146 (4) ◽  
pp. 1096-1112 ◽  
Author(s):  
Fan Ding ◽  
Hansjörg Geiges
Keyword(s):  
Fundamental Group ◽  
Rotation Number ◽  
Contact Structure ◽  
Alternative Proof ◽  
Contact Structures ◽  
Legendrian Knots ◽  
Contact Topology ◽  
Tight Contact ◽  
Contact Surgery

AbstractAs shown by Gluck in 1962, the diffeotopy group of S1×S2 is isomorphic to ℤ2⊕ℤ2 ⊕ℤ2. Here an alternative proof of this result is given, relying on contact topology. We then discuss two applications to contact topology: (i) it is shown that the fundamental group of the space of contact structures on S1×S2, based at the standard tight contact structure, is isomorphic to ℤ; (ii) inspired by previous work of Fraser, an example is given of an integer family of Legendrian knots in S1×S2#S1×S2 (with its standard tight contact structure) that can be distinguished with the help of contact surgery, but not by the classical invariants (topological knot type, Thurston–Bennequin invariant, and rotation number).

scholarly journals On the mean Euler characteristic of contact manifolds

2014 ◽  
Vol 25 (05) ◽  
pp. 1450046 ◽  
Author(s):  
Jacqueline Espina
Keyword(s):  
Euler Characteristic ◽  
Contact Structure ◽  
Broad Class ◽  
Contact Manifolds ◽  
Contact Surgery ◽  
The Mean

We express the mean Euler characteristic (MEC) of a contact structure in terms of the mean indices of closed Reeb orbits for a broad class of contact manifolds, the so-called asymptotically finite contact manifolds. We show that this class is closed under subcritical contact surgery and examine the behavior of the MEC under such surgery. To this end, we revisit the notion of index-positivity for contact forms. We also obtain an expression for the MEC in the Morse–Bott case.

scholarly journals Contact surgery and symplectic handlebodies

1991 ◽  
Vol 20 (2) ◽  
pp. 241-251 ◽  
Author(s):  
Alan WEINSTEIN
Keyword(s):  
Contact Surgery

scholarly journals Applications of contact surgery

Topology ◽  
1997 ◽  
Vol 36 (6) ◽  
pp. 1193-1220 ◽  
Author(s):  
Hansjörg Geiges
Keyword(s):  
Contact Surgery
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