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On growth rate and contact homology

Abstract : It is a conjecture of Colin and Honda that the number of Reeb periodic 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 non-hyperbolic 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 non-isomorphic contact structures for which the number of Reeb periodic orbits of any non-degenerate 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 non-hyperbolic cases that exhibit polynomial growth, namely those of universally tight contact structures non-transverse to the fibers on a circle bundle.
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Contributor : Anne Vaugon Connect in order to contact the contributor
Submitted on : Sunday, October 5, 2014 - 3:19:02 PM
Last modification on : Sunday, November 27, 2022 - 2:48:05 PM
Long-term archiving on: : Friday, April 14, 2017 - 2:52:48 PM


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  • HAL Id : hal-00682399, version 2
  • ARXIV : 1203.5589



Anne Vaugon. On growth rate and contact homology. Algebraic and Geometric Topology, 2015, 15 (2), pp.623--666. ⟨hal-00682399v2⟩



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