Contact structures on product five-manifolds and fibre sums along circles

Hansjörg Geiges, András I. Stipsicz

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Abstract

Two constructions of contact manifolds are presented: (i) products of S1 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 CP2 × S1 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 Z2.

Original languageEnglish
Pages (from-to)195-210
Number of pages16
JournalMathematische Annalen
Volume348
Issue number1
DOIs
Publication statusPublished - Sep 1 2010

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ASJC Scopus subject areas

  • Mathematics(all)

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