Algebraic & Geometric Topology

Classification of tight contact structures on small Seifert fibered $L$–spaces

Irena Matkovič

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Abstract

We identify tight contact structures on small Seifert fibered L –spaces as exactly the structures having nonvanishing contact invariant, and classify them by their induced Spin c structures. The result (in the new case of M ( 1 ; r 1 , r 2 , r 3 ) ) is based on the translation between convex surface theory and the tightness criterion of Lisca and Stipsicz.

Article information

Source
Algebr. Geom. Topol., Volume 18, Number 1 (2018), 111-152.

Dates
Received: 29 January 2016
Revised: 30 March 2017
Accepted: 3 July 2017
First available in Project Euclid: 1 February 2018

Permanent link to this document
https://projecteuclid.org/euclid.agt/1517454213

Digital Object Identifier
doi:10.2140/agt.2018.18.111

Mathematical Reviews number (MathSciNet)
MR3748240

Zentralblatt MATH identifier
06828001

Subjects
Primary: 57R17: Symplectic and contact topology

Keywords
Seifert fibered $3$–manifolds tight contact structures contact Ozsváth–Szabó invariant convex surface theory

Citation

Matkovič, Irena. Classification of tight contact structures on small Seifert fibered $L$–spaces. Algebr. Geom. Topol. 18 (2018), no. 1, 111--152. doi:10.2140/agt.2018.18.111. https://projecteuclid.org/euclid.agt/1517454213


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References

  • F Ding, H Geiges, A I Stipsicz, Surgery diagrams for contact $3$–manifolds, Turkish J. Math. 28 (2004) 41–74
  • Y Eliashberg, Contact $3$–manifolds twenty years since J Martinet's work, Ann. Inst. Fourier $($Grenoble$)$ 42 (1992) 165–192
  • P Ghiggini, On tight contact structures with negative maximal twisting number on small Seifert manifolds, Algebr. Geom. Topol. 8 (2008) 381–396
  • P Ghiggini, P Lisca, A I Stipsicz, Classification of tight contact structures on small Seifert $3$–manifolds with $e_0\geq 0$, Proc. Amer. Math. Soc. 134 (2006) 909–916
  • P Ghiggini, P Lisca, A I Stipsicz, Tight contact structures on some small Seifert fibered $3$–manifolds, Amer. J. Math. 129 (2007) 1403–1447
  • P Ghiggini, S Schönenberger, On the classification of tight contact structures, from “Topology and geometry of manifolds” (G Matić, C McCrory, editors), Proc. Sympos. Pure Math. 71, Amer. Math. Soc., Providence, RI (2003) 121–151
  • K Honda, On the classification of tight contact structures, I, Geom. Topol. 4 (2000) 309–368
  • K Honda, On the classification of tight contact structures, II, J. Differential Geom. 55 (2000) 83–143
  • A G Lecuona, P Lisca, Stein fillable Seifert fibered $3$–manifolds, Algebr. Geom. Topol. 11 (2011) 625–642
  • P Lisca, G Matić, Tight contact structures and Seiberg–Witten invariants, Invent. Math. 129 (1997) 509–525
  • P Lisca, A I Stipsicz, Ozsváth–Szabó invariants and tight contact $3$–manifolds, III, J. Symplectic Geom. 5 (2007) 357–384
  • P Lisca, A I Stipsicz, Ozsváth–Szabó invariants and tight contact three-manifolds, II, J. Differential Geom. 75 (2007) 109–141
  • P Lisca, A I Stipsicz, On the existence of tight contact structures on Seifert fibered $3$–manifolds, Duke Math. J. 148 (2009) 175–209
  • I Matkovič, Fillability of small Seifert fibered spaces, preprint (2016)
  • P Ozsváth, Z Szabó, On the Floer homology of plumbed three-manifolds, Geom. Topol. 7 (2003) 185–224
  • P Ozsváth, Z Szabó, Heegaard Floer homology and contact structures, Duke Math. J. 129 (2005) 39–61
  • O Plamenevskaya, Contact structures with distinct Heegaard Floer invariants, Math. Res. Lett. 11 (2004) 547–561
  • A I Stipsicz, Ozsváth–Szabó invariants and $3$–dimensional contact topology, from “Proceedings of the International Congress of Mathematicians, II” (R Bhatia, A Pal, G Rangarajan, V Srinivas, M Vanninathan, editors), Hindustan Book Agency, New Delhi (2010) 1159–1178
  • C Wendl, Strongly fillable contact manifolds and $J$–holomorphic foliations, Duke Math. J. 151 (2010) 337–384
  • H Wu, Legendrian vertical circles in small Seifert spaces, Commun. Contemp. Math. 8 (2006) 219–246