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

Destabilizing amalgamated Heegaard splittings

Jennifer Schultens and Richard Weidmann

Geometry & Topology Monographs 12 (2007) 319–334

DOI: 10.2140/gtm.2007.12.319

Bibliography
1 D Bachman, Connected sums of unstabilized Heegaard splittings are unstabilized, preprint
2 D Bachman, S Schleimer, E Sedgwick, Sweepouts of amalgamated 3–manifolds, Algebr. Geom. Topol. 6 (2006) 171–194 MR2199458
3 G Burde, H Zieschang, Knots, de Gruyter Studies in Mathematics 5, Walter de Gruyter & Co. (1985) MR808776
4 J Hempel, 3-Manifolds, Ann. of Math. Studies 86, Princeton University Press (1976) MR0415619
5 W Jaco, Lectures on three-manifold topology, CBMS Regional Conference Series in Mathematics 43, American Mathematical Society (1980) MR565450
6 K Johannson, Topology and combinatorics of 3–manifolds, Lecture Notes in Mathematics 1599, Springer (1995) MR1439249
7 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
8 M Lackenby, The Heegaard genus of amalgamated 3–manifolds, Geom. Dedicata 109 (2004) 139–145 MR2113191
9 W B R Lickorish, An introduction to knot theory, Graduate Texts in Mathematics 175, Springer (1997) MR1472978
10 M Lustig, Y Moriah, Generalized Montesinos knots, tunnels and N–torsion, Math. Ann. 295 (1993) 167–189 MR1198847
11 R Qiu, Stabilizations of reducible Heegaard splittings, preprint
12 D Rolfsen, Knots and links, Mathematics Lecture Series 7, Publish or Perish (1976) MR0515288
13 M Scharlemann, J Schultens, Annuli in generalized Heegaard splittings and degeneration of tunnel number, Math. Ann. 317 (2000) 783–820 MR1777119
14 M Scharlemann, A Thompson, Heegaard splittings of (surface)×I are standard, Math. Ann. 295 (1993) 549–564 MR1204837
15 J Schultens, Additivity of bridge numbers of knots, Math. Proc. Cambridge Philos. Soc. 135 (2003) 539–544 MR2018265
16 J Schultens, Heegaard genus formula for Haken manifolds, Geom. Dedicata 119 (2006) 49–68 MR2247647