Algebraic & Geometric Topology Volume 20, issue 4 (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

Pseudo-Anosov maps with small stretch factors on punctured surfaces

Mehdi Yazdi

Algebraic & Geometric Topology 20 (2020) 2095–2128

DOI: 10.2140/agt.2020.20.2095

Bibliography

1	I Agol, C J Leininger, D Margalit, Pseudo-Anosov stretch factors and homology of mapping tori, J. Lond. Math. Soc. 93 (2016) 664 MR3509958
2	P Arnoux, J C Yoccoz, Construction de difféomorphismes pseudo-Anosov, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981) 75 MR610152
3	M Bauer, An upper bound for the least dilatation, Trans. Amer. Math. Soc. 330 (1992) 361 MR1094556
4	C Boissy, E Lanneau, Pseudo-Anosov homeomorphisms on translation surfaces in hyperelliptic components have large entropy, Geom. Funct. Anal. 22 (2012) 74 MR2899683
5	A J Casson, S A Bleiler, Automorphisms of surfaces after Nielsen and Thurston, 9, Cambridge Univ. Press (1988) MR964685
6	J H Cho, J Y Ham, The minimal dilatation of a genus-two surface, Experiment. Math. 17 (2008) 257 MR2455699
7	S Dowdall, Dilatation versus self-intersection number for point-pushing pseudo-Anosov homeomorphisms, J. Topol. 4 (2011) 942 MR2860347
8	B Farb, C J Leininger, D Margalit, The lower central series and pseudo-Anosov dilatations, Amer. J. Math. 130 (2008) 799 MR2418928
9	A Fathi, F Laudenbach, V Poénaru, editors, Travaux de Thurston sur les surfaces, 66–67, Soc. Math. France (1979) 284 MR568308
10	A Fathi, M Shub, Some dynamics of pseudo-Anosov diffeomorphisms MR568308
11	D Fried, Fibrations over S¹ with pseudo-Anosov monodromy MR568308
12	D Fried, Flow equivalence, hyperbolic systems and a new zeta function for flows, Comment. Math. Helv. 57 (1982) 237 MR684116
13	D Fried, Transitive Anosov flows and pseudo-Anosov maps, Topology 22 (1983) 299 MR710103
14	F R Gantmacher, Applications of the theory of matrices, Interscience (1959) MR0107648
15	J Y Ham, W T Song, The minimum dilatation of pseudo-Anosov 5–braids, Experiment. Math. 16 (2007) 167 MR2339273
16	E Hironaka, Penner sequences and asymptotics of minimum dilatations for subfamilies of the mapping class group, Topology Proc. 44 (2014) 315 MR3151755
17	E Hironaka, Small dilatation pseudo-Anosov mapping classes and short circuits on train track automata, preprint (2014) arXiv:1403.2987
18	E Hironaka, E Kin, A family of pseudo-Anosov braids with small dilatation, Algebr. Geom. Topol. 6 (2006) 699 MR2240913
19	S Hirose, E Kin, The asymptotic behavior of the minimal pseudo-Anosov dilatations in the hyperelliptic handlebody groups, Q. J. Math. 68 (2017) 1035 MR3698306
20	H Iwaniec, On the problem of Jacobsthal, Demonstratio Math. 11 (1978) 225 MR499895
21	E Jacobsthal, Über Sequenzen ganzer Zahlen, von denen keine zu n teilerfremd ist, I, Norske Vid. Selsk. Forh. Trondheim 33 (1961) 117 MR0125047
22	E Jacobsthal, Über Sequenzen ganzer Zahlen, von denen keine zu n teilerfremd ist, II, Norske Vid. Selsk. Forh. Trondheim 33 (1961) 125 MR0125047
23	E Jacobsthal, Über Sequenzen ganzer Zahlen, von denen keine zu n teilerfremd ist, III, Norske Vid. Selsk. Forh. Trondheim 33 (1961) 132 MR0125047
24	E Lanneau, J L Thiffeault, On the minimum dilatation of braids on punctured discs, Geom. Dedicata 152 (2011) 165 MR2795241
25	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
26	C J Leininger, D Margalit, On the number and location of short geodesics in moduli space, J. Topol. 6 (2013) 30 MR3029420
27	L Liechti, Minimal dilatation in Penner’s construction, Proc. Amer. Math. Soc. 145 (2017) 3941 MR3665045
28	L Liechti, B Strenner, Minimal Penner dilatations on nonorientable surfaces, J. Topol. Anal. (2019)
29	L Liechti, B Strenner, Minimal pseudo-Anosov stretch factors on nonoriented surfaces, Algebr. Geom. Topol. 20 (2020) 451 MR4071380
30	M Loving, Least dilatation of pure surface braids, Algebr. Geom. Topol. 19 (2019) 941 MR3924180
31	J Malestein, A Putman, Pseudo-Anosov dilatations and the Johnson filtration, Groups Geom. Dyn. 10 (2016) 771 MR3513117
32	B Martelli, An introduction to geometric topology, CreateSpace (2016)
33	S Matsumoto, Topological entropy and Thurston’s norm of atoroidal surface bundles over the circle, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34 (1987) 763 MR927609
34	C T McMullen, Polynomial invariants for fibered 3–manifolds and Teichmüller geodesics for foliations, Ann. Sci. École Norm. Sup. 33 (2000) 519 MR1832823
35	C T McMullen, Entropy and the clique polynomial, J. Topol. 8 (2015) 184 MR3335252
36	H Minakawa, Examples of pseudo-Anosov homeomorphisms with small dilatations, J. Math. Sci. Univ. Tokyo 13 (2006) 95 MR2277516
37	D A Neumann, 3–Manifolds fibering over S¹, Proc. Amer. Math. Soc. 58 (1976) 353 MR413105
38	J Nielsen, Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen, Acta Math. 50 (1927) 189 MR1555256
39	J Nielsen, Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen, II, Acta Math. 53 (1929) 1 MR1555290
40	J Nielsen, Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen, III, Acta Math. 58 (1932) 87 MR1555345
41	J Nielsen, Abbildungsklassen endlicher Ordnung, Acta Math. 75 (1943) 23 MR13306
42	J Nielsen, Surface transformation classes of algebraically finite type, Danske Vid. Selsk. Mat.-Fys. Medd. 21 (1944) MR15791
43	J P Otal, The hyperbolization theorem for fibered 3–manifolds, 7, Amer. Math. Soc. (2001) MR1855976
44	R C Penner, A construction of pseudo-Anosov homeomorphisms, Trans. Amer. Math. Soc. 310 (1988) 179 MR930079
45	R C Penner, Bounds on least dilatations, Proc. Amer. Math. Soc. 113 (1991) 443 MR1068128
46	W T Song, Upper and lower bounds for the minimal positive entropy of pure braids, Bull. London Math. Soc. 37 (2005) 224 MR2119022
47	W T Song, K H Ko, J E Los, Entropies of braids, J. Knot Theory Ramifications 11 (2002) 647 MR1915500
48	W P Thurston, A norm for the homology of 3–manifolds, Mem. Amer. Math. Soc. 339, Amer. Math. Soc. (1986) 99 MR823443
49	W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. 19 (1988) 417 MR956596
50	W P Thurston, Hyperbolic Structures on 3–manifolds, II : Surface groups and 3–manifolds which fiber over the circle, preprint (1998) arXiv:math/9801045
51	J L Tollefson, 3–Manifolds fibering over S¹ with nonunique connected fiber, Proc. Amer. Math. Soc. 21 (1969) 79 MR236945
52	C Y Tsai, The asymptotic behavior of least pseudo-Anosov dilatations, Geom. Topol. 13 (2009) 2253 MR2507119
53	A D Valdivia, Sequences of pseudo-Anosov mapping classes and their asymptotic behavior, New York J. Math. 18 (2012) 609 MR2967106
54	M Yazdi, Lower bound for dilatations, J. Topol. 11 (2018) 602 MR3830877