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On subcritically Stein fillable 5-manifolds

  • Fan Ding,
    School of Mathematical Sciences and LMAM, Peking University, Beijing 100871, P. R. China
  • Hansjörg Geiges,
    Mathematisches Institut, Universität zu Köln, Weyertal 86--90, 50931 Köln, Germany
  • Guangjian Zhang,
    School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China
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Abstract

We make some elementary observations concerning subcritically Stein fillable contact structures on $5$-manifolds. Specifically, we determine the diffeomorphism type of such contact manifolds in the case the fundamental group is finite cyclic, and we show that on the $5$-sphere the standard contact structure is the unique subcritically fillable one. More generally, it is shown that subcritically fillable contact structures on simply connected $5$-manifolds are determined by their underlying almost contact structure. Along the way, we discuss the homotopy classification of almost contact structures.
Keywords: subcritically Stein fillable, 5-manifold, almost contact structure, thickening subcritically Stein fillable, 5-manifold, almost contact structure, thickening
MSC Classifications: 53D35, 32Q28, 57M20, 57Q10, 57R17 show english descriptions Global theory of symplectic and contact manifolds [See also 57Rxx]
Stein manifolds
Two-dimensional complexes
Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28]
Symplectic and contact topology
53D35 - Global theory of symplectic and contact manifolds [See also 57Rxx]
32Q28 - Stein manifolds
57M20 - Two-dimensional complexes
57Q10 - Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28]
57R17 - Symplectic and contact topology
 

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