Algebraic & Geometric Topology Volume 13, issue 5 (2013)

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Obtaining genus $2$ Heegaard splittings from Dehn surgery

Kenneth L Baker, Cameron Gordon and John Luecke

Algebraic & Geometric Topology 13 (2013) 2471–2634

DOI: 10.2140/agt.2013.13.2471

Bibliography

1	K L Baker, Small genus knots in lens spaces have small bridge number, Algebr. Geom. Topol. 6 (2006) 1519 MR2253458
2	K L Baker, C M Gordon, J Luecke, Bridge number and integral Dehn surgery arXiv:1303.7018
3	K L Baker, C M Gordon, J Luecke, Bridge number, Heegaard genus and non-integral Dehn surgery arXiv:1202.0263
4	J Berge, Some knots with surgeries yielding lens spaces, unpublished manuscript
5	S Boyer, X Zhang, On Culler–Shalen seminorms and Dehn filling, Ann. of Math. 148 (1998) 737 MR1670053
6	G E Bredon, J W Wood, Non-orientable surfaces in orientable $3$–manifolds, Invent. Math. 7 (1969) 83 MR0246312
7	A J Casson, C M Gordon, Reducing Heegaard splittings, Topology Appl. 27 (1987) 275 MR918537
8	J C Cha, C Livingston, KnotInfo: Table of Knot Invariants (2010)
9	M Culler, C M Gordon, J Luecke, P B Shalen, Dehn surgery on knots, Bull. Amer. Math. Soc. 13 (1985) 43 MR788388
10	M Eudave Muñoz, On nonsimple $3$–manifolds and $2$–handle addition, Topology Appl. 55 (1994) 131 MR1256216
11	G K Francis, On knot-spanning surfaces: An illustrated essay on topological art, from: "The visual mind" (editor M Emmer), MIT Press (1993) 57 MR1255839
12	C Frohman, One-sided incompressible surfaces in Seifert fibered spaces, Topology Appl. 23 (1986) 103 MR855450
13	D Gabai, Foliations and the topology of $3$–manifolds, III, J. Differential Geom. 26 (1987) 479 MR910018
14	H Goda, M Teragaito, Dehn surgeries on knots which yield lens spaces and genera of knots, Math. Proc. Cambridge Philos. Soc. 129 (2000) 501 MR1780501
15	C M Gordon, Combinatorial methods in Dehn surgery, from: "Lectures at KNOTS" (editor S Suzuki), Ser. Knots Everything 15, World Sci. Publ., River Edge, NJ (1997) 263 MR1474525
16	C M Gordon, R A Litherland, Incompressible planar surfaces in $3$–manifolds, Topology Appl. 18 (1984) 121 MR769286
17	C M Gordon, R A Litherland, Incompressible surfaces in branched coverings, from: "The Smith conjecture" (editors J W Morgan, H Bass), Pure Appl. Math. 112, Academic Press (1984) 139 MR758466
18	C M Gordon, J Luecke, Only integral Dehn surgeries can yield reducible manifolds, Math. Proc. Cambridge Philos. Soc. 102 (1987) 97 MR886439
19	C M Gordon, J Luecke, Knots are determined by their complements, J. Amer. Math. Soc. 2 (1989) 371 MR965210
20	C M Gordon, J Luecke, Dehn surgeries on knots creating essential tori, I, Comm. Anal. Geom. 3 (1995) 597 MR1371211
21	C M Gordon, J Luecke, Dehn surgeries on knots creating essential tori, II, Comm. Anal. Geom. 8 (2000) 671 MR1792371
22	C M Gordon, J Luecke, Non-integral toroidal Dehn surgeries, Comm. Anal. Geom. 12 (2004) 417 MR2074884
23	W Haken, Some results on surfaces in $3$–manifolds, from: "Studies in Modern Topology" (editor P Hilton), Math. Assoc. Amer. (1968) 39 MR0224071
24	A E Hatcher, On the boundary curves of incompressible surfaces, Pacific J. Math. 99 (1982) 373 MR658066
25	J Hempel, $3$–manifolds as viewed from the curve complex, Topology 40 (2001) 631 MR1838999
26	M Lackenby, R Meyerhoff, The maximal number of exceptional Dehn surgeries, Invent. Math. 191 (2013) 341 MR3010379
27	Y N Minsky, Y Moriah, S Schleimer, High distance knots, Algebr. Geom. Topol. 7 (2007) 1471 MR2366166
28	Y Moriah, H Rubinstein, Heegaard structures of negatively curved $3$–manifolds, Comm. Anal. Geom. 5 (1997) 375 MR1487722
29	K Morimoto, M Sakuma, Y Yokota, Identifying tunnel number one knots, J. Math. Soc. Japan 48 (1996) 667 MR1404816
30	Y Rieck, Heegaard structures of manifolds in the Dehn filling space, Topology 39 (2000) 619 MR1746912
31	Y Rieck, E Sedgwick, Finiteness results for Heegaard surfaces in surgered manifolds, Comm. Anal. Geom. 9 (2001) 351 MR1846207
32	Y Rieck, E Sedgwick, Persistence of Heegaard structures under Dehn filling, Topology Appl. 109 (2001) 41 MR1804562
33	M Scharlemann, Local detection of strongly irreducible Heegaard splittings, Topology Appl. 90 (1998) 135 MR1648310
34	M Teragaito, A Seifert fibered manifold with infinitely many knot-surgery descriptions, Int. Math. Res. Not. 2007 (2007) MR2347296
35	A Thompson, Thin position and bridge number for knots in the $3$–sphere, Topology 36 (1997) 505 MR1415602
36	A Thompson, The disjoint curve property and genus $2$ manifolds, Topology Appl. 97 (1999) 273 MR1711418
37	M Tomova, Distance of Heegaard splittings of knot complements, Pacific J. Math. 236 (2008) 119 MR2398991
38	H F Trotter, Non-invertible knots exist, Topology 2 (1963) 275 MR0158395