Volume 7, issue 2 (2007)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 19
Issue 7, 3217–3753
Issue 6, 2677–3215
Issue 5, 2151–2676
Issue 4, 1619–2150
Issue 3, 1079–1618
Issue 2, 533–1078
Issue 1, 1–532

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

Author Index
The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
To Appear
 
Other MSP Journals
On non-compact Heegaard splittings

Scott A Taylor

Algebraic & Geometric Topology 7 (2007) 603–672
Bibliography
1 D Bachman, S Schleimer, E Sedgwick, Sweepouts of amalgamated 3-manifolds, Algebr. Geom. Topol. 6 (2006) 171 MR2199458
2 M Boileau, J P Otal, Sur les scindements de Heegaard du tore $T^3$, J. Differential Geom. 32 (1990) 209 MR1064873
3 F Bonahon, Cobordism of automorphisms of surfaces, Ann. Sci. École Norm. Sup. $(4)$ 16 (1983) 237 MR732345
4 F Bonahon, J P Otal, Scindements de Heegaard des espaces lenticulaires, Ann. Sci. École Norm. Sup. $(4)$ 16 (1983) MR740078
5 M G Brin, T L Thickstun, Open, irreducible $3$-manifolds which are end $1$-movable, Topology 26 (1987) 211 MR895574
6 E M Brown, Unknotting in $M^{2}\times I$, Trans. Amer. Math. Soc. 123 (1966) 480 MR0198482
7 E M Brown, T W Tucker, On proper homotopy theory for noncompact $3$-manifolds, Trans. Amer. Math. Soc. 188 (1974) 105 MR0334225
8 R D Canary, D McCullough, Homotopy equivalences of 3-manifolds and deformation theory of Kleinian groups, Mem. Amer. Math. Soc. 172 (2004) MR2096234
9 A J Casson, C M Gordon, Reducing Heegaard splittings, Topology Appl. 27 (1987) 275 MR918537
10 M Eudave Muñoz, Y Uchida, Non-simple links with tunnel number one, Proc. Amer. Math. Soc. 124 (1996) 1567 MR1328348
11 M H Freedman, An unknotting result for complete minimal surfaces [in] $\mathbb{R}^3$, Invent. Math. 109 (1992) 41 MR1168364
12 C Frohman, The topological uniqueness of triply periodic minimal surfaces in $\mathbb{R}^3$, J. Differential Geom. 31 (1990) 277 MR1030674
13 C Frohman, W H Meeks III, The topological uniqueness of complete one-ended minimal surfaces and Heegaard surfaces in $\mathbb{R}^3$, J. Amer. Math. Soc. 10 (1997) 495 MR1443545
14 C Frohman, W H Meeks III, The topological classification of minimal surfaces in $\mathbb{R}^3$ arXiv:math.DG/0209286
15 J Hempel, 3-manifolds, AMS Chelsea Publishing, Providence, RI (2004) MR2098385
16 W Jaco, Lectures on three-manifold topology, CBMS Regional Conference Series in Mathematics 43, Amer. Math. Soc. (1980) MR565450
17 W H Meeks, H Rosenberg, The theory of minimal surfaces in $M{\times}\mathbb{R}$, Comment. Math. Helv. 80 (2005) 811 MR2182702
18 J T Pitts, J H Rubinstein, Applications of minimax to minimal surfaces and the topology of 3–manifolds, from: "Miniconference on geometry and partial differential equations, 2 (Canberra, 1986)", Proc. Centre Math. Anal. Austral. Nat. Univ. 12, Austral. Nat. Univ. (1987) 137 MR924434
19 F Raymond, The end point compactification of manifolds, Pacific J. Math. 10 (1960) 947 MR0120637
20 T Saito, M Scharlemann, J Schultens, Lecture notes on generalized Heegaard splittings arXiv:math.GT/0504167
21 M Scharlemann, Heegaard splittings of compact 3–manifolds, from: "Handbook of geometric topology", North-Holland (2002) 921 MR1886684
22 M Scharlemann, J Schultens, Comparing Heegaard and JSJ structures of orientable 3–manifolds, Trans. Amer. Math. Soc. 353 (2001) 557 MR1804508
23 M Scharlemann, A Thompson, Heegaard splittings of $(\mathrm{surface}){\times}I$ are standard, Math. Ann. 295 (1993) 549 MR1204837
24 M Scharlemann, A Thompson, Thin position and Heegaard splittings of the 3–sphere, J. Differential Geom. 39 (1994) 343 MR1267894
25 J Schultens, The classification of Heegaard splittings for $(\mathrm{compact orientable surface}){\times}S^1$, Proc. London Math. Soc. $(3)$ 67 (1993) 425 MR1226608
26 P Scott, Fundamental groups of non-compact 3–manifolds, Proc. London Math. Soc. $(3)$ 34 (1977) 303 MR0448333
27 W P Thurston, Three-dimensional geometry and topology. Vol. 1, Princeton Mathematical Series 35, Princeton University Press MR1435975
28 F Waldhausen, Heegaard–Zerlegungen der 3–Sphäre, Topology 7 (1968) 195 MR0227992