Orbit growth of contact structures after surgery
| Autor: | Anne Vaugon, Boris Hasselblatt, Patrick Foulon |
|---|---|
| Přispěvatelé: | Centre International de Rencontres Mathématiques (CIRM), Aix Marseille Université (AMU)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics, Tufts University, Tufts University, Tufts University [Medford]-Tufts University [Medford], Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Boris Hasselblatt partially supported by the Committee on Faculty Research Awards of Tufts University., ANR-16-CE40-0017,Quantact,Topologie quantique et géométrie de contact(2016) |
| Rok vydání: | 2021 |
| Předmět: |
Anosov flow
medicine.medical_specialty Dynamical systems theory Contact geometry [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] Ocean Engineering Context (language use) Dynamical Systems (math.DS) Homology (mathematics) Reeb flow 01 natural sciences surgery Intersection 0103 physical sciences FOS: Mathematics medicine Mathematics - Dynamical Systems 0101 mathematics Mathematics::Symplectic Geometry 3-manifold Mathematics contact structure 010102 general mathematics contact homology Mathematics::Geometric Topology [MATH.MATH-SG]Mathematics [math]/Symplectic Geometry [math.SG] Surgery Flow (mathematics) Mathematics - Symplectic Geometry Orbit (dynamics) Symplectic Geometry (math.SG) 010307 mathematical physics |
| Zdroj: | Annales Henri Lebesgue. 4:1103-1141 |
| ISSN: | 2644-9463 |
| Popis: | This work is at the intersection of dynamical systems and contact geometry, and it focuses on the effects of a contact surgery adapted to the study of Reeb fields and on the effects of invariance of contact homology. We show that this contact surgery produces an increased dynamical complexity for all Reeb flows compatible with the new contact structure. We study Reeb Anosov fields on closed 3manifolds that are not topologically orbit-equivalent to any algebraic flow; this includes many examples on hyperbolic 3-manifolds. Our study also includes results of exponential growth in cases where neither the flow nor the manifold obtained by surgery is hyperbolic, as well as results when the original flow is periodic. This work fully demonstrates, in this context, the relevance of contact homology to the analysis of the dynamics of Reeb fields. |
| Databáze: | OpenAIRE |
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