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Commentarii Mathematici Helvetici

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Volume 94, Issue 3, 2019, pp. 569–622
DOI: 10.4171/CMH/468

Published online: 2019-09-25

Dynamically exotic contact spheres in dimensions $\geq 7$

Marcelo R.R. Alves[1] and Matthias Meiwes[2]

(1) Université libre de Bruxelles, Belgium
(2) RWTH Aachen, Germany

We exhibit the first examples of contact structures on $S^{2n-1}$ with $n\geq 4$ and on $S^3\times S^2$, all equipped with their standard smooth structures, for which every Reeb flow has positive topological entropy. As a new technical tool for the study of the volume growth of Reeb flows we introduce the notion of algebraic growth of wrapped Floer homology. Its power stems from its stability under several geometric operations on Liouville domains.

Keywords: Topological entropy, contact structure, Reeb dynamics, Floer homology

Alves Marcelo, Meiwes Matthias: Dynamically exotic contact spheres in dimensions $\geq 7$. Comment. Math. Helv. 94 (2019), 569-622. doi: 10.4171/CMH/468