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On growth rate and
contact homology
Anne Vaugon |
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Algebraic & Geometric Topology 15 (2015) 623–666
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Abstract |
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A conjecture of Colin and Honda states that the number of periodic Reeb orbits of universally tight contact structures on hyperbolic manifolds grows exponentially with the period, and they speculate further that the growth rate of contact homology is polynomial on nonhyperbolic geometries. Along the line of the conjecture, for manifolds with a hyperbolic component that fibers on the circle, we prove that there are infinitely many nonisomorphic contact structures for which the number of periodic Reeb orbits of any nondegenerate Reeb vector field grows exponentially. Our result hinges on the exponential growth of contact homology, which we derive as well. We also compute contact homology in some nonhyperbolic cases that exhibit polynomial growth, namely those of universally tight contact structures on a circle bundle nontransverse to the fibers. |
Keywords
contact geometry, Reeb vector field, contact homology,
growth rate
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Mathematical Subject Classification 2010
Primary: 57R17
Secondary: 53C15, 57M50
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References |
Publication
Received: 25 March 2012
Revised: 21 September 2014
Accepted: 28 September 2014
Published: 22 April 2015
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Authors |
| Anne Vaugon | |
| Laboratoire de Mathématiques Jean
Leray 2, rue de la Houssinière BP 92208 44322 Nantes Cedex 3 France |
Département de Mathématiques
d’Orsay Université Paris-Sud Bâtiment 425 Faulté des Sciences d’Orsay 91405 Orsay Cedex France |
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