Algebraic & Geometric Topology Volume 20, issue 1 (2020)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Minimal pseudo-Anosov stretch factors on nonoriented surfaces

Livio Liechti and Balázs Strenner

Algebraic & Geometric Topology 20 (2020) 451–485

DOI: 10.2140/agt.2020.20.451

Bibliography

1	J W Aaber, N Dunfield, Closed surface bundles of least volume, Algebr. Geom. Topol. 10 (2010) 2315 MR2745673
2	C C Adams, The noncompact hyperbolic 3–manifold of minimal volume, Proc. Amer. Math. Soc. 100 (1987) 601 MR894423
3	I Agol, Volume change under drilling, Geom. Topol. 6 (2002) 905 MR1943385
4	I Agol, P A Storm, W P Thurston, Lower bounds on volumes of hyperbolic Haken 3–manifolds, J. Amer. Math. Soc. 20 (2007) 1053 MR2328715
5	P Arnoux, J C Yoccoz, Construction de difféomorphismes pseudo-Anosov, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981) 75 MR610152
6	M Bauer, An upper bound for the least dilatation, Trans. Amer. Math. Soc. 330 (1992) 361 MR1094556
7	R Breusch, On the distribution of the roots of a polynomial with integral coefficients, Proc. Amer. Math. Soc. 2 (1951) 939 MR45246
8	J H Cho, J Y Ham, The minimal dilatation of a genus-two surface, Experiment. Math. 17 (2008) 257 MR2455699
9	D Gabai, R Meyerhoff, P Milley, Minimum volume cusped hyperbolic three-manifolds, J. Amer. Math. Soc. 22 (2009) 1157 MR2525782
10	E Hironaka, Small dilatation mapping classes coming from the simplest hyperbolic braid, Algebr. Geom. Topol. 10 (2010) 2041 MR2728483
11	E Hironaka, E Kin, A family of pseudo-Anosov braids with small dilatation, Algebr. Geom. Topol. 6 (2006) 699 MR2240913
12	N V Ivanov, Coefficients of expansion of pseudo-Anosov homeomorphisms, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. 167 (1988) 111 MR964259
13	E Kin, S Kojima, M Takasawa, Entropy versus volume for pseudo-Anosovs, Experiment. Math. 18 (2009) 397 MR2583541
14	E Kin, M Takasawa, Pseudo-Anosovs on closed surfaces having small entropy and the Whitehead sister link exterior, J. Math. Soc. Japan 65 (2013) 411 MR3055592
15	S Kojima, G McShane, Normalized entropy versus volume for pseudo-Anosovs, Geom. Topol. 22 (2018) 2403 MR3784525
16	E Lanneau, J L Thiffeault, On the minimum dilatation of braids on punctured discs, Geom. Dedicata 152 (2011) 165 MR2795241
17	E Lanneau, J L Thiffeault, On the minimum dilatation of pseudo-Anosov homeromorphisms on surfaces of small genus, Ann. Inst. Fourier (Grenoble) 61 (2011) 105 MR2828128
18	C J Leininger, On groups generated by two positive multi-twists : Teichmüller curves and Lehmer’s number, Geom. Topol. 8 (2004) 1301 MR2119298
19	L Liechti, On the arithmetic and the geometry of skew-reciprocal polynomials, Proc. Amer. Math. Soc. 147 (2019) 5131 MR4021075
20	L Liechti, B Strenner, The Arnoux–Yoccoz mapping classes via Penner’s construction, preprint (2018) arXiv:1805.01248
21	L Liechti, B Strenner, Minimal Penner dilatations on nonorientable surfaces, J. Topol. Anal. (2019)
22	C T McMullen, Polynomial invariants for fibered 3–manifolds and Teichmüller geodesics for foliations, Ann. Sci. École Norm. Sup. 33 (2000) 519 MR1832823
23	C T McMullen, Billiards and Teichmüller curves on Hilbert modular surfaces, J. Amer. Math. Soc. 16 (2003) 857 MR1992827
24	P Milley, Minimum volume hyperbolic 3–manifolds, J. Topol. 2 (2009) 181 MR2499442
25	H Minakawa, Examples of pseudo-Anosov homeomorphisms with small dilatations, J. Math. Sci. Univ. Tokyo 13 (2006) 95 MR2277516
26	R C Penner, A construction of pseudo-Anosov homeomorphisms, Trans. Amer. Math. Soc. 310 (1988) 179 MR930079
27	R C Penner, Bounds on least dilatations, Proc. Amer. Math. Soc. 113 (1991) 443 MR1068128
28	A Schinzel, H Zassenhaus, A refinement of two theorems of Kronecker, Michigan Math. J. 12 (1965) 81 MR175882
29	H Shin, B Strenner, Pseudo-Anosov mapping classes not arising from Penner’s construction, Geom. Topol. 19 (2015) 3645 MR3447112
30	B Strenner, Algebraic degrees of pseudo-Anosov stretch factors, Geom. Funct. Anal. 27 (2017) 1497 MR3737368
31	B Strenner, Lifts of pseudo-Anosov homeomorphisms of nonorientable surfaces have vanishing SAF invariant, Math. Res. Lett. 25 (2018) 677 MR3826841
32	W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988) 417 MR956596
33	C Y Tsai, The asymptotic behavior of least pseudo-Anosov dilatations, Geom. Topol. 13 (2009) 2253 MR2507119
34	A D Valdivia, Sequences of pseudo-Anosov mapping classes and their asymptotic behavior, New York J. Math. 18 (2012) 609 MR2967106
35	M Yazdi, Pseudo-Anosov maps with small stretch factors on punctured surfaces, preprint (2018) arXiv:1801.01754
36	A Y Zhirov, On the minimum dilation of pseudo-Anosov diffeomorphisms of a double torus, Uspekhi Mat. Nauk 50 (1995) 197 MR1331364