scholarly journals The Foliated Weinstein Conjecture

2017 ◽  
Vol 2018 (16) ◽  
pp. 5148-5177 ◽  
Author(s):  
Álvaro del Pino ◽  
Francisco Presas
Keyword(s):  
Weinstein Conjecture

Symplectic capacities

2017 ◽  
Author(s):  
Dusa McDuff ◽  
Dietmar Salamon
Keyword(s):  
Euclidean Space ◽  
Generating Functions ◽  
Weinstein Conjecture ◽  
Finite Dimensional ◽  
Hofer Metric

This chapter returns to the problems which were formulated in Chapter 1, namely the Weinstein conjecture, the nonsqueezing theorem, and symplectic rigidity. These questions are all related to the existence and properties of symplectic capacities. The chapter begins by discussing some of the consequences which follow from the existence of capacities. In particular, it establishes symplectic rigidity and discusses the relation between capacities and the Hofer metric on the group of Hamiltonian symplectomorphisms. The chapter then introduces the Hofer–Zehnder capacity, and shows that its existence gives rise to a proof of the Weinstein conjecture for hypersurfaces of Euclidean space. The last section contains a proof that the Hofer–Zehnder capacity satisfies the required axioms. This proof translates the Hofer–Zehnder variational argument into the setting of (finite-dimensional) generating functions.

scholarly journals The Weinstein conjecture for stable Hamiltonian structures

2009 ◽  
Vol 13 (2) ◽  
pp. 901-941 ◽  
Author(s):  
Michael Hutchings ◽  
Clifford Henry Taubes
Keyword(s):  
Hamiltonian Structures ◽  
Weinstein Conjecture

scholarly journals OPEN BOOKS AND THE WEINSTEIN CONJECTURE

2014 ◽  
Vol 65 (3) ◽  
pp. 869-885 ◽  
Author(s):  
M. Dorner ◽  
H. Geiges ◽  
K. Zehmisch
Keyword(s):  
Open Books ◽  
Weinstein Conjecture

The Weinstein conjecture inP×C 1

1990 ◽  
Vol 203 (1) ◽  
pp. 469-482 ◽  
Author(s):  
A. Floer ◽  
H. Hofer ◽  
C. Viterbo
Keyword(s):  
Weinstein Conjecture

scholarly journals Polyfolds, cobordisms, and the strong Weinstein conjecture

2017 ◽  
Vol 305 ◽  
pp. 1250-1267 ◽  
Author(s):  
Stefan Suhr ◽  
Kai Zehmisch
Keyword(s):  
Weinstein Conjecture

scholarly journals EXPLICIT HORIZONTAL OPEN BOOKS ON SOME PLUMBINGS

2006 ◽  
Vol 17 (09) ◽  
pp. 1013-1031 ◽  
Author(s):  
TOLGA ETGÜ ◽  
BURAK OZBAGCI
Keyword(s):  
Contact Structure ◽  
Complex Surface ◽  
Contact Structures ◽  
Open Book ◽  
Open Books ◽  
Tight Contact ◽  
Weinstein Conjecture ◽  
Circle Bundles ◽  
Surface Singularities

We describe explicit open books on arbitrary plumbings of oriented circle bundles over closed oriented surfaces. We show that, for a non-positive plumbing, the open book we construct is horizontal and the corresponding compatible contact structure is also horizontal and Stein fillable. In particular, on some Seifert fibered 3-manifolds we describe open books which are horizontal with respect to their plumbing description. As another application we describe horizontal open books isomorphic to Milnor open books for some complex surface singularities. Moreover we give examples of tight contact 3-manifolds supported by planar open books. As a consequence, the Weinstein conjecture holds for these tight contact structures [1].

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