scholarly journals Non-commutative geometry and symplectic field theory

2007 ◽  
Vol 361 (6) ◽  
pp. 464-471 ◽  
Author(s):  
R.G.G. Amorim ◽  
M.C.B. Fernandes ◽  
F.C. Khanna ◽  
A.E. Santana ◽  
J.D.M. Vianna
Keyword(s):  
Field Theory ◽  
Symplectic Field Theory

scholarly journals Introduction to Symplectic Field Theory

2000 ◽  
pp. 560-673 ◽  
Author(s):  
Y. Eliashberg ◽  
A. Glvental ◽  
H. Hofer
Keyword(s):  
Field Theory ◽  
Symplectic Field Theory

scholarly journals Local contact homology and applications

2015 ◽  
Vol 07 (02) ◽  
pp. 167-238 ◽  
Author(s):  
Umberto L. Hryniewicz ◽  
Leonardo Macarini
Keyword(s):  
Field Theory ◽  
Periodic Orbit ◽  
Periodic Orbits ◽  
Local Version ◽  
Contact Homology ◽  
Local Contact ◽  
Symplectic Field Theory ◽  
Uniformly Bounded

We introduce a local version of contact homology for an isolated periodic orbit of the Reeb flow and prove that its rank is uniformly bounded for isolated iterations. Several applications are obtained, including a generalization of Gromoll–Meyer's theorem on the existence of infinitely many simple periodic orbits, resonance relations and conditions for the existence of non-hyperbolic periodic orbits. Most of the results of this paper remain conjectural until the foundational issues of Symplectic Field Theory are resolved.

scholarly journals SFT COMPUTATIONS AND INTERSECTION THEORY IN HIGHER-DIMENSIONAL CONTACT MANIFOLDS

2021 ◽  
pp. 1-52
Author(s):  
Agustin Moreno
Keyword(s):  
Field Theory ◽  
Intersection Theory ◽  
Holomorphic Curves ◽  
Perturbation Scheme ◽  
Contact Manifolds ◽  
Higher Dimensional ◽  
Symplectic Field Theory ◽  
Phd Thesis ◽  
Symplectic Cobordisms

Abstract I construct infinitely many nondiffeomorphic examples of $5$ -dimensional contact manifolds which are tight, admit no strong fillings and do not have Giroux torsion. I obtain obstruction results for symplectic cobordisms, for which I give a proof not relying on the polyfold abstract perturbation scheme for Symplectic Field Theory (SFT). These results are part of my PhD thesis [23], and are the first applications of higher-dimensional Siefring intersection theory for holomorphic curves and hypersurfaces, as outlined in [23, 24], as a prequel to [30].

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