Volume 14 (2008)

Download this article
For screen
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
All Volumes
 
About this Series
Ethics Statement
Purchase Printed Copies
Author Index
ISSN 1464-8997 (online)
ISSN 1464-8989 (print)
 
MSP Books and Monographs
Other MSP Publications

Epimorphisms between 2–bridge link groups

Tomotada Ohtsuki, Robert Riley and Makoto Sakuma

Geometry & Topology Monographs 14 (2008) 417–450

DOI: 10.2140/gtm.2008.14.417

Bibliography
1 H Akiyoshi, M Sakuma, M Wada, Y Yamashita, Punctured torus groups and 2–bridge knot groups. I, Lecture Notes in Mathematics 1909, Springer (2007) MR2330319
2 M Boileau, J Porti, Geometrization of 3–orbifolds of cyclic type, Astérisque (2001) 208 MR1844891 Appendix A by Michael Heusener and Porti
3 M Boileau, S Wang, Nonzero degree maps and surface bundles over S1, J. Differential Geom. 43 (1996) 789–806 MR1412685
4 M Boileau, S Wang, J Rubinstein, Finiteness of 3–manifolds associated with nonzero degree mappings arXiv:math.GT/0511541
5 B H Bowditch, Markoff triples and quasi-Fuchsian groups, Proc. London Math. Soc. (3) 77 (1998) 697–736 MR1643429
6 M Brittenham, Y Q Wu, The classification of exceptional Dehn surgeries on 2–bridge knots, Comm. Anal. Geom. 9 (2001) 97–113 MR1807953
7 G Burde, H Zieschang, Knots, de Gruyter Studies in Mathematics 5, Walter de Gruyter & Co. (1985) MR808776
8 D Cooper, C D Hodgson, S P Kerckhoff, Three-dimensional orbifolds and cone-manifolds, MSJ Memoirs 5, Mathematical Society of Japan (2000) MR1778789 With a postface by Sadayoshi Kojima
9 R H Crowell, R H Fox, Introduction to knot theory, Graduate Texts in Mathematics 57, Springer (1977) MR0445489 Reprint of the 1963 original
10 M Culler, P B Shalen, Varieties of group representations and splittings of 3–manifolds, Ann. of Math. (2) 117 (1983) 109–146 MR683804
11 T Eguchi, Markoff maps and 2–bridge knot groups (Japanese), dissertation, Osaka University (2003)
12 F González-Acuña, A Ramírez, Two-bridge knots with property Q, Q. J. Math. 52 (2001) 447–454 MR1874490
13 F González-Acuña, A Ramírez, Epimorphisms of knot groups onto free products, Topology 42 (2003) 1205–1227 MR1981354
14 C M Gordon, Ribbon concordance of knots in the 3–sphere, Math. Ann. 257 (1981) 157–170 MR634459
15 A Hatcher, W Thurston, Incompressible surfaces in 2–bridge knot complements, Invent. Math. 79 (1985) 225–246 MR778125
16 J Hempel, 3–Manifolds, Ann. of Math. Studies 86, Princeton University Press (1976) MR0415619
17 T Honma, On the 3–dimensional Poincaré conjecture, Sūgaku 42 (1990) 74–80 MR1046374
18 L H Kauffman, S Lambropoulou, On the classification of rational knots, Enseign. Math. (2) 49 (2003) 357–410 MR2028021
19 A Kawauchi, A survey of knot theory, Birkhäuser Verlag (1996) MR1417494 Translated and revised from the 1990 Japanese original by the author
20 A Kawauchi, Topological imitations, from: "Lectures at KNOTS '96 (Tokyo)", Ser. Knots Everything 15, World Sci. Publ., River Edge, NJ (1997) 19–37 MR1474517
21 L Keen, C Series, The Riley slice of Schottky space, Proc. London Math. Soc. (3) 69 (1994) 72–90 MR1272421
22 R Kirby, editor, Problems in low-dimensional topology, from: "Geometric topology (Athens, GA, 1993)", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 35–473 MR1470751
23 T Kitano, M Suzuki, A partial order in the knot table, Experiment. Math. 14 (2005) 385–390 MR2193401
24 T Kitano, M Suzuki, A partial order in the knot table (II), preprint (2008)
25 T Kitano, M Suzuki, M Wada, Twisted Alexander polynomials and surjectivity of a group homomorphism, Algebr. Geom. Topol. 5 (2005) 1315–1324 MR2171811
26 Y Komori, C Series, The Riley slice revisited, from: "The Epstein birthday schrift" (editors I Rivin, C Rourke, C Series), Geom. Topol. Monogr. 1 (1998) 303–316 MR1668296
27 G McShane, Simple geodesics and a series constant over Teichmuller space, Invent. Math. 132 (1998) 607–632 MR1625712
28 K Miyazaki, Ribbon concordance does not imply a degree one map, Proc. Amer. Math. Soc. 108 (1990) 1055–1058 MR994781
29 T Ohtsuki, Ideal points and incompressible surfaces in two-bridge knot complements, J. Math. Soc. Japan 46 (1994) 51–87 MR1248091
30 T Ohtsuki, R Riley, Representations of 2–bridge knot groups on 2-bridge knot groups (1993) unfinished draft
31 A W Reid, S C Wang, Q Zhou, Generalized Hopfian property, a minimal Haken manifold, and epimorphisms between 3–manifold groups, Acta Math. Sin. (Engl. Ser.) 18 (2002) 157–172 MR1894848
32 R Riley, Parabolic representations of knot groups. I, Proc. London Math. Soc. (3) 24 (1972) 217–242 MR0300267
33 R Riley, Nonabelian representations of 2–bridge knot groups, Quart. J. Math. Oxford Ser. (2) 35 (1984) 191–208 MR745421
34 R Riley, Algebra for Heckoid groups, Trans. Amer. Math. Soc. 334 (1992) 389–409 MR1107029
35 D Rolfsen, Knots and links, Math. Lecture Series 7, Publish or Perish (1976) MR0515288
36 M Sakuma, Variations of McShane's identity for the Riley slice and 2–bridge links, Sūrikaisekikenkyūsho Kōkyūroku (1999) 103–108 MR1744474 Hyperbolic spaces and related topics (Japanese) (Kyoto, 1998)
37 H Schubert, Knoten mit zwei Brücken, Math. Z. 65 (1956) 133–170 MR0082104
38 P B Shalen, Representations of 3–manifold groups, from: "Handbook of geometric topology", North-Holland (2002) 955–1044 MR1886685
39 L Siebenmann, Exercices sur les noeuds rationnels (1972) unpublished
40 D S Silver, W Whitten, Knot group epimorphisms, J. Knot Theory Ramifications 15 (2006) 153–166 MR2207903
41 T Soma, Nonzero degree maps to hyperbolic 3–manifolds, J. Differential Geom. 49 (1998) 517–546 MR1669645
42 T Soma, Epimorphism sequences between hyperbolic 3–manifold groups, Proc. Amer. Math. Soc. 130 (2002) 1221–1223 MR1873800
43 S Wang, Nonzero degree maps between 3–manifolds, from: "Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002)", Higher Ed. Press (2002) 457–468 MR1957056
44 J Weeks, SnapPea: a program for creating and studying hyperbolic 3–manifolds