Algebraic & Geometric Topology Volume 9, issue 4 (2009)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Other MSP journals

Amalgamations of Heegaard splittings in $3$–manifolds without some essential surfaces

Guoqiu Yang and Fengchun Lei

Algebraic & Geometric Topology 9 (2009) 2041–2054

DOI: 10.2140/agt.2009.9.2041

Bibliography

1	D Bachman, S Schleimer, E Sedgwick, Sweepouts of amalgamated 3–manifolds, Algebr. Geom. Topol. 6 (2006) 171 MR2199458
2	K Hartshorn, Heegaard splittings of Haken manifolds have bounded distance, Pacific J. Math. 204 (2002) 61 MR1905192
3	J Hempel, 3–manifolds, 86, Princeton Univ. Press (1976) MR0415619
4	J Hempel, 3–manifolds as viewed from the curve complex, Topology 40 (2001) 631 MR1838999
5	W Jaco, Lectures on three-manifold topology, 43, Amer. Math. Soc. (1980) MR565450
6	T Kobayashi, R Qiu, The amalgamation of high distance Heegaard splittings is always efficient, Math. Ann. 341 (2008) 707 MR2399167
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 MR2103921
8	M Lackenby, The Heegaard genus of amalgamated 3–manifolds, Geom. Dedicata 109 (2004) 139 MR2113191
9	F Lei, G Yang, A lower bound of genus of amalgamations of Heegaard splittings, Math. Proc. Cambridge Philos. Soc. 146 (2009) 615 MR2496347
10	T Li, On the Heegaard splittings of amalgamated 3–manifolds, from: "Workshop on Heegaard Splittings" (editors C Gordon, Y Moriah), Geom. Topol. Monogr. 12 (2007) 157 MR2408246
11	M Scharlemann, Local detection of strongly irreducible Heegaard splittings, Topology Appl. 90 (1998) 135 MR1648310
12	M Scharlemann, Proximity in the curve complex: boundary reduction and bicompressible surfaces, Pacific J. Math. 228 (2006) 325 MR2274524
13	M Scharlemann, A Thompson, Thin position for 3–manifolds, from: "Geometric topology (Haifa, 1992)" (editors C Gordon, Y Moriah, B Wajnryb), Contemp. Math. 164, Amer. Math. Soc. (1994) 231 MR1282766
14	M Scharlemann, M Tomova, Alternate Heegaard genus bounds distance, Geom. Topol. 10 (2006) 593 MR2224466
15	J Schultens, The classification of Heegaard splittings for (compact orientable surface) ×S¹, Proc. London Math. Soc. (3) 67 (1993) 425 MR1226608
16	J Schultens, Additivity of tunnel number for small knots, Comment. Math. Helv. 75 (2000) 353 MR1793793
17	J Schultens, R Weidmann, Destabilizing amalgamated Heegaard splittings, from: "Workshop on Heegaard Splittings" (editors C Gordon, Y Moriah), Geom. Topol. Monogr. 12 (2007) 319 MR2408253
18	J Souto, Distances in the curve complex and Heegaard genus, Preprint (2003)
19	G Yang, F Lei, On amalgamations of Heegaard splittings with high distance, Proc. Amer. Math. Soc. 137 (2009) 723 MR2448595