A Smale Type Result and Applications to Contact Homology

Autori

  • Vittorio Martino Università di Bologna

DOI:

https://doi.org/10.6092/issn.2240-2829/4718

Parole chiave:

Contact Morse Homology, Legendrian loops

Abstract

In questa nota mostreremo che l'inclusione di un opportuno sottospazio dello spazio dei cappi Legendriani nello spazio totale dei cappi è un'equivalenza omotopica S1-equivariante. Inoltre, poiché il primo sottospazio è lo spazio delle variazioni di un dato funzionale azione, calcoleremo l'omologia di contatto per una famiglia di forme di contatto tight sul toro tridimensionale.

Riferimenti bibliografici

A. Bahri, Compactness, Adv. Nonlinear Stud. 8 (2008), no. 3, 465-568

A.Bahri, Homology computation, Adv. Nonlinear Stud. 8 (2008), no. 1, 1-7

A. Bahri, Pseudo-orbits of contact forms, Pitman Research Notes in Mathematics Series 173, Longman Scientific and Technical, Longman, London, 1988

A. Bahri, A Lagrangian Method for the Periodic Orbit Problem of Reeb Vector-Fields, Geometric Methods in PDE's, 1-19, Lect. Notes Semin. Interdiscip. Mat., 7, Semin. Interdiscip. Mat. (S.I.M.), Potenza, 2008

A. Bahri, Classical and Quantic Periodic Motions of Multiply Polarized Spin-particles, Pitman Research Notes in Mathematics Series, 378. Longman, Harlow, 1998

A. Bahri, Flow lines and algebraic invariants in contact form geometry, Progress in Nonlinear Differential Equations and their Applications, 53. Birkhuser Boston, Inc., Boston, MA, 2003

A. Bahri, Classical and quantic periodic motions of multiply polarized spin-particles, Pitman Research Notes in Mathematics Series, 378. Longman, Harlow, 1998

A. Bahri; Y. Xu, Recent progress in conformal geometry, ICP Advanced Texts in Mathematics, 1. Imperial College Press, London, 2007

F. Bourgeois, A Morse-Bott approach to Contact Homology, in "Symplectic and Contact Topology: Interactions and Perspectives", Fields Institute Communications 35 (2003), 55-77

F. Bourgeois, V. Colin, Homologie de contact des variétés toroïdales, Geometry and Topology 9 (2005), 299-313

Y. Eliashberg, Classification of overtwisted contact structures on 3-manifolds, Invent. Math. 98 (1989), no. 3, 623-637

E. Giroux, Une infinit de structures de contact tendues sur une infinit de varits, Invent. Math. 135 (1999), no. 3, 789-802

H. Geiges; J. Gonzalo, Contact geometry and complex surfaces, Invent. Math. 121 (1995), no. 1, 147-209

J. Gonzalo, A dynamical characterization of contact circles, Geom. Dedicata 132 (2008), 105-119

J. Gonzalo, F.Varela, Modèles globaux des variétés de contact, Third Schnepfenried geometry conference, Vol.1 (Schnepfenried, 1982), Astérisque, no.107-108, pp. 163-168, Soc. Math.France, Paris, 1983

Y. Kanda, The classification of tight contact structures on the 3-torus, Comm. Anal. Geom. 5 (1997), 413-438

E.B. Lebow, Embedded contact homology of 2-torus bundles over the circle. Thesis (Ph.D.), University of California, Berkeley. 2007. 165 pp

A. Maalaoui, V. Martino. The topology of a subspace of the Legendrian curves on a closed contact 3-manifold, Advanced Nonlinear Studies, 14 (2014), 393-426

A. Maalaoui, V. Martino. Homology computation for a class of contact structures on T3, Calculus of Variations and Partial Differential Equations, 50 (2014), 599-614

V. Martino, A Legendre transform on an exotic S3, Advanced Nonlinear Studies, 11 (2011), 145-156

S. Smale, Regular curves on Riemannian manifolds. Trans. Amer. Math. Soc. 87 (1958), 492-512

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Pubblicato

2014-12-30

Come citare

Martino, V. (2014). A Smale Type Result and Applications to Contact Homology. Bruno Pini Mathematical Analysis Seminar, 5(1), 45–56. https://doi.org/10.6092/issn.2240-2829/4718

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