Geodesic
Algebraic degrees of stretch factors in mapping class groups
Shin, Hyunshik1
1Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea
Algebraic and Geometric Topology, Tome 16 (2016) no. 3, pp. 1567-1584
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

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.

DOI : 10.2140/agt.2016.16.1567
Classification : 57M50, 57M15
Keywords: pseudo-Anosov, stretch factor, dilatation, algebraic degree, Salem number

Shin, Hyunshik  1

1 Department of Mathematical Sciences, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, South Korea 
@article{10_2140_agt_2016_16_1567,
     author = {Shin, Hyunshik},
     title = {Algebraic degrees of stretch factors in mapping class groups},
     journal = {Algebraic and Geometric Topology},
     pages = {1567--1584},
     year = {2016},
     volume = {16},
     number = {3},
     doi = {10.2140/agt.2016.16.1567},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2016.16.1567/}
}
TY  - JOUR
AU  - Shin, Hyunshik
TI  - Algebraic degrees of stretch factors in mapping class groups
JO  - Algebraic and Geometric Topology
PY  - 2016
SP  - 1567
EP  - 1584
VL  - 16
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2016.16.1567/
DO  - 10.2140/agt.2016.16.1567
ID  - 10_2140_agt_2016_16_1567
ER  - 
%0 Journal Article
%A Shin, Hyunshik
%T Algebraic degrees of stretch factors in mapping class groups
%J Algebraic and Geometric Topology
%D 2016
%P 1567-1584
%V 16
%N 3
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2016.16.1567/
%R 10.2140/agt.2016.16.1567
%F 10_2140_agt_2016_16_1567
Shin, Hyunshik. Algebraic degrees of stretch factors in mapping class groups. Algebraic and Geometric Topology, Tome 16 (2016) no. 3, pp. 1567-1584. doi: 10.2140/agt.2016.16.1567

[1] P Arnoux, J C Yoccoz, Construction de difféomorphismes pseudo-Anosov, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981) 75

[2] P Brinkmann, An implementation of the Bestvina–Handel algorithm for surface homeomorphisms, Experiment. Math. 9 (2000) 235

[3] B Farb, D Margalit, A primer on mapping class groups, 49, Princeton Univ. Press (2012)

[4] D Fried, Growth rate of surface homeomorphisms and flow equivalence, Ergodic Theory Dynam. Systems 5 (1985) 539

[5] 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

[6] C J Leininger, On groups generated by two positive multi-twists : Teichmüller curves and Lehmer’s number, Geom. Topol. 8 (2004) 1301

[7] M Lepović, I Gutman, Some spectral properties of starlike trees, Bull. Cl. Sci. Math. Nat. Sci. Math. 122 (2001) 107

[8] D D Long, Constructing pseudo-Anosov maps, from: "Knot theory and manifolds" (editor D Rolfsen), Lecture Notes in Math. 1144, Springer (1985) 108

[9] J F Mckee, P Rowlinson, C J Smyth, Salem numbers and Pisot numbers from stars, from: "Number theory in progress, Vol. 1" (editors K Györy, H Iwaniec, J Urbanowicz), de Gruyter (1999) 309

[10] L Neuwirth, N Patterson, A sequence of pseudo-Anosov diffeomorphisms, from: "Combinatorial group theory and topology" (editors S M Gersten, S J R.), Ann. of Math. Stud. 111, Princeton Univ. Press (1987) 443

[11] H Shin, Spectral radius of a star with one long arm, preprint (2015)

[12] W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988) 417

Cité par Sources :