Mathematical Research Letters

Volume 24 (2017)

Number 6

Hyperbolic rational homology spheres not admitting fillable contact structures

Pages: 1693 – 1705



Amey Kaloti (Department of Mathematics, University of Iowa, Iowa City, Ia., U.S.A.)

Bülent Tosun (Department of Mathematics, University of Alabama, Tuscaloosa, Al., U.S.A.)


In this paper, we exhibit an infinite family of hyperbolic rational homology $3$-spheres which do not admit any fillable contact structures. We also note that most of these manifolds do admit tight contact structures.

Received 30 April 2016

Accepted 9 February 2017

Published 29 January 2018