ON STABILIZERS OF SOME TEICHMÜLLER DISKS IN POINTED MAPPING CLASS GROUPS
Glasgow mathematical journal, Tome 52 (2010) no. 3, pp. 593-604

Voir la notice de l'article provenant de la source Cambridge University Press

We prove that for each Riemann surface of finite analytic type (p, n) with p ≥ 2, there exist uncountably many Teichmüller disks Δ in the Teichmüller space T(S), where S = - {a point a}, with these properties: (1) the natural projection j: T(S) → T() defined by forgetting a induces an isometric embedding of each Δ into T(); and (2) the stabilizer of each Teichmüller disk Δ in the a-pointed mapping class group of S is trivial.
DOI : 10.1017/S0017089510000455
Mots-clés : 30C60, 30F60
ZHANG, C. ON STABILIZERS OF SOME TEICHMÜLLER DISKS IN POINTED MAPPING CLASS GROUPS. Glasgow mathematical journal, Tome 52 (2010) no. 3, pp. 593-604. doi: 10.1017/S0017089510000455
@article{10_1017_S0017089510000455,
     author = {ZHANG, C.},
     title = {ON {STABILIZERS} {OF} {SOME} {TEICHM\"ULLER} {DISKS} {IN} {POINTED} {MAPPING} {CLASS} {GROUPS}},
     journal = {Glasgow mathematical journal},
     pages = {593--604},
     year = {2010},
     volume = {52},
     number = {3},
     doi = {10.1017/S0017089510000455},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000455/}
}
TY  - JOUR
AU  - ZHANG, C.
TI  - ON STABILIZERS OF SOME TEICHMÜLLER DISKS IN POINTED MAPPING CLASS GROUPS
JO  - Glasgow mathematical journal
PY  - 2010
SP  - 593
EP  - 604
VL  - 52
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000455/
DO  - 10.1017/S0017089510000455
ID  - 10_1017_S0017089510000455
ER  - 
%0 Journal Article
%A ZHANG, C.
%T ON STABILIZERS OF SOME TEICHMÜLLER DISKS IN POINTED MAPPING CLASS GROUPS
%J Glasgow mathematical journal
%D 2010
%P 593-604
%V 52
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000455/
%R 10.1017/S0017089510000455
%F 10_1017_S0017089510000455

[1] 1.Abikoff, W., The real analytic theory of Teichmüller spaces, Lecture notes in mathematics 820 (Springer-Verlag, Berlin–New York, 1980). Google Scholar

[2] 2.Ahlfors, L. V. and Bers, L., Riemann's mapping theorem for variable metrics, Ann. Math. 72 (2) (1960), 385–404. Google Scholar | DOI

[3] 3.Arnoux, P. and Yoccoz, J. C., Construction de diffeomorphismes pseudo-Anosov, C. R. Acad. Sci. Paris Sr. I Math. 292 (1) (1981), 75–78. Google Scholar

[4] 4.Beardon, A., The geometry of discrete groups (Springer-Verlag, New York, 1983). Google Scholar | DOI

[5] 5.Bers, L., Fiber spaces over Teichmüller spaces, Acta Math. 130 (1973), 89–126. Google Scholar | DOI

[6] 6.Bers, L., An extremal problem for quasiconformal mappings and a theorem by Thurston, Acta Math. 141 (1978), 73–98. Google Scholar

[7] 7.Earle, C. J. and Gardiner, F., Teichmüller disks and Veech's -structures, Contemp. Math. 201 (1997), 165–189. Google Scholar

[8] 8.Hubert, P. and Lanneau, E., Veech group without parabolic elements, Duke Math. J. 133 (2006), 335–346. Google Scholar | DOI

[9] 9.Farkas, H. M. and Kra, I., Riemann surfaces (Springer-Verlag, New York, 1980). Google Scholar | DOI

[10] 10.Kerckhoff, S. P., The Nielsen realisation problem, Ann. Math. 117 (1983), 235–265. Google Scholar | DOI

[11] 11.Kra, I., On the Nielsen–Thurston–Bers type of some self-maps of Riemann surfaces, Acta Math. 146 (1981), 231–270. Google Scholar | DOI

[12] 12.Kravetz, S., On the geometry of Teichmüller spaces and the structure of their modular groups, Ann. Acad. Sci. Fenn. Math. 278 (1959), 135. Google Scholar

[13] 13.Kenyon, R. and Smillie, J., Billiards in rational-angled triangles, Comment. Math, Helv. 75 (2000), 65–108. Google Scholar

[14] 14.Purzitsky, N., A cutting and pasting of noncompact polygons with applications to Fuchsian groups, Acta Math. 143 (1979), 233–250. Google Scholar

[15] 15.Strebel, K., Quadratic differentials (Springer-Verlag, Berlin, 1984). Google Scholar

[16] 16.Thurston, W. P., On the geometry and dynamics of diffeomorphisms of surfaces. Bull. Amer. Math. Soc. (N.S.) 19 (1988), 417–431. Google Scholar | DOI

[17] 17.Veech, W. A., Teichmüller curves in moduli space, Einstein series and an application to triangular billiards. Invent. Math. 97 (1989), 553–583. Google Scholar | DOI

Cité par Sources :