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On Subcritically Stein Fillable 5-manifolds

Published online by Cambridge University Press:  20 November 2018

Fan Ding ,
Hansjörg Geiges  and
Guangjian Zhang
Fan Ding
Affiliation:
School of Mathematical Sciences and LMAM, Peking University, Beijing 100871, P. R. China, e-mail: dingfan@math.pku.edu.cn
Hansjörg Geiges
Affiliation:
Mathematisches Institut, Universität zu Köln, Weyertal 86–90, 50931 K?ln, Germany, e-mail: geiges@math.uni-koeln.de
Guangjian Zhang
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China, e-mail: zhangguangjian8888@163.com
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Abstract

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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 where 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

53D3532Q2857M2057Q1057R17subcritically Stein fillable5-manifoldalmost contact structurethickening
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 1 , 01 March 2018 , pp. 85 - 96
Copyright
Copyright © Canadian Mathematical Society 2018

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