We show that for all n >= 3, any (2n + 1)-dimensional manifold that admits a tight contact structure also admits a tight but non-fillable contact structure, in the same almost contact class. For n = 2, we obtain the same result provided that the first Chern class vanishes. We further construct Liouville but not Weinstein fillable contact structures on any Weinstein fillable contact manifold of dimension at least 7 with torsion first Chern class.
Publication:
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
http://dx.doi.org/10.4171/jems/1787
Author:
Jonathan Bowden
Institute for Differential Geometry, Leibniz University Hannover, 30167 Hannover, Germany
jonathan.bowden@math.uni-hannover.de
Fabio Gironella
Faculté des Sciences et des Techniques, CNRS - Nantes Université, 44200 Nantes, France
Agustin Moreno
Heidelberg University, 69120 Heidelberg, Germany
Zhengyi Zhou
State Key Laboratory of Mathematical Sciences, Morningside Center of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing, P. R. China
zhyzhou@amss.ac.cn
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