Contact structures on product five-manifolds and fibre sums along circles |
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Authors: | Hansjörg Geiges András I Stipsicz |
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Institution: | (1) Faculty of Mathematics, University of Bucharest, 14 Academiei str., 70109 Bucharest, Romania;(2) Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, Bucharest, Romania;(3) Department of Mathematics, University of Glasgow, 15 University Gardens, Glasgow, Scotland;(4) Institute of Theoretical and Experimental Physics, B. Cheremushkinskaya, 25, Moscow, 117259, Russia |
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Abstract: | Two constructions of contact manifolds are presented: (i) products of S
1 with manifolds admitting a suitable decomposition into two exact symplectic pieces and (ii) fibre connected sums along isotropic
circles. Baykur has found a decomposition as required for (i) for all closed, oriented 4-manifolds. As a corollary, we can
show that all closed, oriented 5-manifolds that are Cartesian products of lower-dimensional manifolds carry a contact structure.
For symplectic 4-manifolds we exhibit an alternative construction of such a decomposition; this gives us control over the
homotopy type of the corresponding contact structure. In particular, we prove that
\mathbb CP2×S1{{\mathbb {CP}}^2\times S^1} admits a contact structure in every homotopy class of almost contact structures. The existence of contact structures is also
established for a large class of 5-manifolds with fundamental group
\mathbbZ2{{\mathbb{Z}}_2} . |
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Keywords: | |
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