Algebraic & Geometric Topology

Algebraic degrees of stretch factors in mapping class groups

Hyunshik Shin

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Abstract

We explicitly construct pseudo-Anosov maps on the closed surface of genus g with orientable foliations whose stretch factor λ is a Salem number with algebraic degree 2g. Using this result, we show that there is a pseudo-Anosov map whose stretch factor has algebraic degree d, for each positive even integer d such that  d g.

Article information

Source
Algebr. Geom. Topol., Volume 16, Number 3 (2016), 1567-1584.

Dates
Received: 25 September 2014
Revised: 16 September 2015
Accepted: 21 September 2015
First available in Project Euclid: 28 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1511895856

Digital Object Identifier
doi:10.2140/agt.2016.16.1567

Mathematical Reviews number (MathSciNet)
MR3523049

Zentralblatt MATH identifier
1356.57017

Subjects
Primary: 57M50: Geometric structures on low-dimensional manifolds 57M15: Relations with graph theory [See also 05Cxx]

Keywords
pseudo-Anosov stretch factor dilatation algebraic degree Salem number

Citation

Shin, Hyunshik. Algebraic degrees of stretch factors in mapping class groups. Algebr. Geom. Topol. 16 (2016), no. 3, 1567--1584. doi:10.2140/agt.2016.16.1567. https://projecteuclid.org/euclid.agt/1511895856


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References

  • P Arnoux, J-C Yoccoz, Construction de difféomorphismes pseudo-Anosov, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981) 75–78
  • P Brinkmann, An implementation of the Bestvina–Handel algorithm for surface homeomorphisms, Experiment. Math. 9 (2000) 235–240
  • B Farb, D Margalit, A primer on mapping class groups, Princeton Mathematical Series 49, Princeton Univ. Press (2012)
  • D Fried, Growth rate of surface homeomorphisms and flow equivalence, Ergodic Theory Dynam. Systems 5 (1985) 539–563
  • E Lanneau, J-L Thiffeault, On the minimum dilatation of pseudo-Anosov homeromorphisms [sic] on surfaces of small genus, Ann. Inst. Fourier $($Grenoble$)$ 61 (2011) 105–144
  • C,J Leininger, On groups generated by two positive multi-twists: Teichmüller curves and Lehmer's number, Geom. Topol. 8 (2004) 1301–1359
  • M Lepović, I Gutman, Some spectral properties of starlike trees, Bull. Cl. Sci. Math. Nat. Sci. Math. 122 (2001) 107–113
  • D,D Long, Constructing pseudo-Anosov maps, from: “Knot theory and manifolds”, (D Rolfsen, editor), Lecture Notes in Math. 1144, Springer, Berlin (1985) 108–114
  • J,F McKee, P Rowlinson, C,J Smyth, Salem numbers and Pisot numbers from stars, from: “Number theory in progress, Vol. 1”, (K Györy, H Iwaniec, J Urbanowicz, editors), de Gruyter, Berlin (1999) 309–319
  • L Neuwirth, N Patterson, A sequence of pseudo-Anosov diffeomorphisms, from: “Combinatorial group theory and topology”, (S,M Gersten, S,J R, editors), Ann. of Math. Stud. 111, Princeton Univ. Press (1987) 443–449
  • H Shin, Spectral radius of a star with one long arm, preprint (2015) To appear in Open J. Discrete Math. Available at \setbox0\makeatletter\@url http://mathsci.kaist.ac.kr/~hshin/papers/starlikelongarm.pdf {\unhbox0
  • W,P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988) 417–431