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We show that Galois conjugates of stretch factors of pseudo-Anosov mapping classes arising from Penner’s construction lie off the unit circle. As a consequence, we show that, for all but a few exceptional surfaces, there are examples of pseudo-Anosov mapping classes so that no power of them arises from Penner’s construction. This resolves a conjecture of Penner.
Shin, Hyunshik 1 ; Strenner, Balázs 2
@article{GT_2015_19_6_a13,
author = {Shin, Hyunshik and Strenner, Bal\'azs},
title = {Pseudo-Anosov mapping classes not arising from {Penner{\textquoteright}s} construction},
journal = {Geometry & topology},
pages = {3645--3656},
publisher = {mathdoc},
volume = {19},
number = {6},
year = {2015},
doi = {10.2140/gt.2015.19.3645},
url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.2015.19.3645/}
}
TY - JOUR AU - Shin, Hyunshik AU - Strenner, Balázs TI - Pseudo-Anosov mapping classes not arising from Penner’s construction JO - Geometry & topology PY - 2015 SP - 3645 EP - 3656 VL - 19 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/gt.2015.19.3645/ DO - 10.2140/gt.2015.19.3645 ID - GT_2015_19_6_a13 ER -
%0 Journal Article %A Shin, Hyunshik %A Strenner, Balázs %T Pseudo-Anosov mapping classes not arising from Penner’s construction %J Geometry & topology %D 2015 %P 3645-3656 %V 19 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/gt.2015.19.3645/ %R 10.2140/gt.2015.19.3645 %F GT_2015_19_6_a13
Shin, Hyunshik; Strenner, Balázs. Pseudo-Anosov mapping classes not arising from Penner’s construction. Geometry & topology, Tome 19 (2015) no. 6, pp. 3645-3656. doi : 10.2140/gt.2015.19.3645. http://geodesic.mathdoc.fr/articles/10.2140/gt.2015.19.3645/
[1] , , Construction de difféomorphismes pseudo-Anosov, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981) 75
[2] , An upper bound for the least dilatation, Trans. Amer. Math. Soc. 330 (1992) 361
[3] , , Train tracks and automorphisms of free groups, Ann. of Math. 135 (1992) 1
[4] , , Automorphisms of surfaces after Nielsen and Thurston, London Math. Soc. Student Texts 9, Cambridge Univ. Press (1988)
[5] , , A primer on mapping class groups, Princeton Mathematical Series 49, Princeton Univ. Press (2012)
[6] , , , editors, Travaux de Thurston sur les surfaces, Astérisque 66, Soc. Math. France (1979) 284
[7] , Small dilatation mapping classes coming from the simplest hyperbolic braid, Algebr. Geom. Topol. 10 (2010) 2041
[8] , On the Nielsen–Thurston–Bers type of some self-maps of Riemann surfaces, Acta Math. 146 (1981) 231
[9] , , On the minimum dilatation of braids on punctured discs, Geom. Dedicata 152 (2011) 165
[10] , , On the minimum dilatation of pseudo-Anosov homeromorphisms [sic] on surfaces of small genus, Ann. Inst. Fourier (Grenoble) 61 (2011) 105
[11] , On groups generated by two positive multi-twists: Teichmüller curves and Lehmer's number, Geom. Topol. 8 (2004) 1301
[12] , Constructing pseudo-Anosov maps, from: "Knot theory and manifolds" (editor D Rolfsen), Lecture Notes in Math. 1144, Springer (1985) 108
[13] , A construction of pseudo-Anosov homeomorphisms, Trans. Amer. Math. Soc. 310 (1988) 179
[14] , Bounds on least dilatations, Proc. Amer. Math. Soc. 113 (1991) 443
[15] , Probing mapping class groups using arcs, from: "Problems on mapping class groups and related topics" (editor B Farb), Proc. Sympos. Pure Math. 74, Amer. Math. Soc. (2006) 97
[16] , Algebraic degrees of stretch factors in mapping class groups, preprint (2015)
[17] , Algebraic degrees and Galois conjugates of pseudo-Anosov stretch factors, preprint (2015)
[18] , On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988) 417
[19] , On the minimum dilation of pseudo-Anosov diffeomorphisms of a double torus, Uspekhi Mat. Nauk 50 (1995) 197
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