Journal of Symplectic Geometry

Volume 12 (2014)

Number 4

A remark on the Reeb flow for spheres

Pages: 657 – 671

DOI: http://dx.doi.org/10.4310/JSG.2014.v12.n4.a1

Authors

Roger Casals (Instituto de Ciencias Matemáticas, CSIC, Madrid, Spain)

Francisco Presas (Instituto de Ciencias Matemáticas, CSIC, Madrid, Spain)

Abstract

We prove the non-triviality of the Reeb flow for the standard contact spheres $\mathbb{S}^{2n+1}, n \neq 3$, inside the fundamental group of their contactomorphism group. The argument uses the existence of homotopically non-trivial $2$-spheres in the space of contact structures of a $3$-Sasakian manifold.

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