Volume 12 (2007)

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

Degeneration of Heegaard genus, a survey

David Bachman and Ryan Derby-Talbot

Geometry & Topology Monographs 12 (2007) 1–15

DOI: 10.2140/gtm.2007.12.1

Bibliography
1 D Bachman, Connected sums of unstabilized Heegaard splittings are unstabilized arXiv:math.GT/0404058
2 D Bachman, S Schleimer, Surface bundles versus Heegaard splittings, Comm. Anal. Geom. 13 (2005) 903–928 MR2216145
3 D Bachman, S Schleimer, E Sedgwick, Sweepouts of amalgamated 3-manifolds, Algebr. Geom. Topol. 6 (2006) 171–194 MR2199458
4 M Boileau, H Zieschang, Heegaard genus of closed orientable Seifert 3–manifolds, Invent. Math. 76 (1984) 455–468 MR746538
5 M Brittenham, Y Rieck, The Heegaard genus of bundles over S¹ arXiv:math.GT/0608517
6 D Cooper, M Scharlemann, The structure of a solvmanifold's Heegaard splittings, from: "Proceedings of 6th Gökova Geometry-Topology Conference", Turkish J. Math. 23 (1999) 1–18 MR1701636
7 W Haken, Some results on surfaces in 3–manifolds, from: "Studies in Modern Topology", Math. Assoc. Amer. (distributed by Prentice-Hall, Englewood Cliffs, N.J.) (1968) 39–98 MR0224071
8 A Hatcher, Notes on Basic 3-Manifold Topology
9 W Jaco, Lectures on three-manifold topology, CBMS Regional Conference Series in Mathematics 43, Amer. Math. Soc. (1980) MR565450
10 K Johannson, Topology and combinatorics of 3-manifolds, Lecture Notes in Mathematics 1599, Springer (1995) MR1439249
11 R Kirby, Problems in low-dimensional topology, from: "Geometric topology (Athens, GA, 1993)", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 35–473 MR1470751
12 T Kobayashi, R Qiu, Y Rieck, S Wang, Separating incompressible surfaces and stabilizations of Heegaard splittings, Math. Proc. Cambridge Philos. Soc. 137 (2004) 633–643 MR2103921
13 M Lackenby, Attaching handlebodies to 3-manifolds, Geom. Topol. 6 (2002) 889–904 MR1943384
14 M Lackenby, The Heegaard genus of amalgamated 3-manifolds, Geom. Dedicata 109 (2004) 139–145 MR2113191
15 M Lackenby, Heegaard splittings, the virtually Haken conjecture and property (τ), Invent. Math. 164 (2006) 317–359 MR2218779
16 T Li, On the Heegaard splittings of amalgamated 3-manifolds arXiv:math.GT/0701395
17 J Milnor, A unique decomposition theorem for 3–manifolds, Amer. J. Math. 84 (1962) 1–7 MR01422125
18 Y Moriah, H Rubinstein, Heegaard structures of negatively curved 3–manifolds, Comm. Anal. Geom. 5 (1997) 375–412 MR1487722
19 Y Moriah, J Schultens, Irreducible Heegaard splittings of Seifert fibered spaces are either vertical or horizontal, Topology 37 (1998) 1089–1112 MR1650355
20 J T Pitts, J H Rubinstein, Existence of minimal surfaces of bounded topological type in three-manifolds, from: "Miniconference on geometry and partial differential equations (Canberra, 1985)", Proc. Centre Math. Anal. Austral. Nat. Univ. 10, Austral. Nat. Univ. (1986) 163–176 MR857665
21 R Qiu, Stabilizations of reducible Heegaard splittings arXiv:math.GT/0409497
22 Y Rieck, Heegaard structures of manifolds in the Dehn filling space, Topology 39 (2000) 619–641 MR1746912
23 Y Rieck, E Sedgwick, Finiteness results for Heegaard surfaces in surgered manifolds, Comm. Anal. Geom. 9 (2001) 351–367 MR1846207
24 Y Rieck, E Sedgwick, Persistence of Heegaard structures under Dehn filling, Topology Appl. 109 (2001) 41–53 MR1804562
25 J H Rubinstein, Minimal surfaces in geometric 3-manifolds, from: "Global theory of minimal surfaces", Clay Math. Proc. 2, Amer. Math. Soc. (2005) 725–746 MR2167286
26 M Scharlemann, Heegaard splittings of compact 3-manifolds, from: "Handbook of geometric topology", North-Holland (2002) 921–953 MR1886684
27 J Schultens, Heegaard genus formula for Haken manifolds, Geom. Dedicata 119 (2006) 49–68 MR2247647
28 J Schultens, R Weidmann, Destabilizing amalgamated Heegaard splittings arXiv:math.GT/0510386
29 E Sedgwick, The irreducibility of Heegaard splittings of Seifert fibered spaces, Pacific J. Math. 190 (1999) 173–199 MR1722770
30 J Souto, Distances in the curve complex and Heegaard genus