Geometry & Topology

Right-veering diffeomorphisms of compact surfaces with boundary II

Ko Honda, William H Kazez, and Gordana Matić

Full-text: Open access

PDF File (410 KB)

Abstract

We continue our study of the monoid of right-veering diffeomorphisms on a compact oriented surface with nonempty boundary, introduced in [Invent. Math. 169 (2007) 427–449]. We conduct a detailed study of the case when the surface is a punctured torus; in particular, we exhibit the difference between the monoid of right-veering diffeomorphisms and the monoid of products of positive Dehn twists, with the help of the Rademacher function. We then generalize to the braid group Bn on n strands by relating the signature and the Maslov index. Finally, we discuss the symplectic fillability in the pseudo-Anosov case by comparing with the work of Roberts [Proc. London Math. Soc. (3) 82/83 (2001) 747–768/443–471].

Article information

Source
Geom. Topol., Volume 12, Number 4 (2008), 2057-2094.

Dates
Received: 6 December 2006
Revised: 22 April 2008
Accepted: 18 June 2008
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513800122

Digital Object Identifier
doi:10.2140/gt.2008.12.2057

Mathematical Reviews number (MathSciNet)
MR2431016

Zentralblatt MATH identifier
1170.57013

Subjects
Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

Keywords
tight contact structure bypass open book decomposition fibered link mapping class group Dehn twists

Citation

Honda, Ko; Kazez, William H; Matić, Gordana. Right-veering diffeomorphisms of compact surfaces with boundary II. Geom. Topol. 12 (2008), no. 4, 2057--2094. doi:10.2140/gt.2008.12.2057. https://projecteuclid.org/euclid.gt/1513800122


Export citation

References

  • J Barge, É Ghys, Cocycles d'Euler et de Maslov, Math. Ann. 294 (1992) 235–265
    Mathematical Reviews (MathSciNet): MR1183404
    Zentralblatt MATH: 0894.55006
    Digital Object Identifier: doi:10.1007/BF01934324
  • Y M Eliashberg, W P Thurston, Confoliations, University Lecture Series 13, Amer. Math. Soc. (1998)
    Mathematical Reviews (MathSciNet): MR1483314
  • J B Etnyre, Legendrian and transversal knots, from: “Handbook of knot theory”, Elsevier B. V., Amsterdam (2005) 105–185
    Mathematical Reviews (MathSciNet): MR2179261
    Zentralblatt MATH: 1095.57006
  • J-M Gambaudo, É Ghys, Commutators and diffeomorphisms of surfaces, Ergodic Theory Dynam. Systems 24 (2004) 1591–1617
    Mathematical Reviews (MathSciNet): MR2104597
    Zentralblatt MATH: 1088.37018
    Digital Object Identifier: doi:10.1017/S0143385703000737
  • J-M Gambaudo, É Ghys, Braids and signatures, Bull. Soc. Math. France 133 (2005) 541–579
    Mathematical Reviews (MathSciNet): MR2233695
    Zentralblatt MATH: 1361.57008
    Digital Object Identifier: doi:10.24033/bsmf.2496
  • É Ghys, Groups acting on the circle, Enseign. Math. $(2)$ 47 (2001) 329–407
    Mathematical Reviews (MathSciNet): MR1876932
    Zentralblatt MATH: 1044.37033
  • E Giroux, Géométrie de contact: de la dimension trois vers les dimensions supérieures, from: “Proc. of the ICM, Vol. II (Beijing, 2002)”, Higher Ed. Press, Beijing (2002) 405–414
    Mathematical Reviews (MathSciNet): MR1957051
  • A Hatcher, Some examples of essential laminations in $3$–manifolds, Ann. Inst. Fourier $($Grenoble$)$ 42 (1992) 313–325
    Mathematical Reviews (MathSciNet): MR1162564
    Zentralblatt MATH: 0759.57006
    Digital Object Identifier: doi:10.5802/aif.1293
  • K Honda, On the classification of tight contact structures. I, Geom. Topol. 4 (2000) 309–368
    Mathematical Reviews (MathSciNet): MR1786111
    Zentralblatt MATH: 0980.57010
    Digital Object Identifier: doi:10.2140/gt.2000.4.309
  • K Honda, W H Kazez, G Matić, On the contact class in Heegaard Floer homology
    arXiv: math.GT/0609734
  • K Honda, W H Kazez, G Matić, Tight contact structures on fibered hyperbolic $3$–manifolds, J. Differential Geom. 64 (2003) 305–358
    Mathematical Reviews (MathSciNet): MR2029907
    Zentralblatt MATH: 1083.53082
    Digital Object Identifier: doi:10.4310/jdg/1102536453
    Project Euclid: euclid.jdg/1102536453
  • K Honda, W H Kazez, G Matić, Right-veering diffeomorphisms of compact surfaces with boundary, Invent. Math. 169 (2007) 427–449
    Mathematical Reviews (MathSciNet): MR2318562
    Zentralblatt MATH: 1167.57008
    Digital Object Identifier: doi:10.1007/s00222-007-0051-4
  • S Y Orevkov, Markov moves for quasipositive braids, C. R. Acad. Sci. Paris Sér. I Math. 331 (2000) 557–562
    Mathematical Reviews (MathSciNet): MR1794098
    Zentralblatt MATH: 0994.57008
    Digital Object Identifier: doi:10.1016/S0764-4442(00)01631-1
  • J Robbin, D Salamon, The Maslov index for paths, Topology 32 (1993) 827–844
    Mathematical Reviews (MathSciNet): MR1241874
    Zentralblatt MATH: 0798.58018
    Digital Object Identifier: doi:10.1016/0040-9383(93)90052-W
  • R Roberts, Taut foliations in punctured surface bundles. I, Proc. London Math. Soc. $(3)$ 82 (2001) 747–768
    Mathematical Reviews (MathSciNet): MR1816696
    Zentralblatt MATH: 1034.57017
    Digital Object Identifier: doi:10.1112/plms/82.3.747
  • R Roberts, Taut foliations in punctured surface bundles. II, Proc. London Math. Soc. $(3)$ 83 (2001) 443–471
    Mathematical Reviews (MathSciNet): MR1839461
    Zentralblatt MATH: 1034.57018
    Digital Object Identifier: doi:10.1112/plms/83.2.443
  • W P Thurston, H E Winkelnkemper, On the existence of contact forms, Proc. Amer. Math. Soc. 52 (1975) 345–347
    Mathematical Reviews (MathSciNet): MR0375366
    Zentralblatt MATH: 0312.53028
    Digital Object Identifier: doi:10.1090/S0002-9939-1975-0375366-7

MSP

Geometry & Topology

New content alerts

Email RSS ToC RSS Article
  • You have access to this content.
  • You have partial access to this content.
  • You do not have access to this content.
Turn Off MathJax

What is MathJax?

More like this

+ See more