Geodesic
Heegaard splittings and the pants complex
Johnson, Jesse1
1Mathematics Department, University of California, Davis, CA 95616, USA
Algebraic and Geometric Topology, Tome 6 (2006) no. 2, pp. 853-874
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We define integral measures of complexity for Heegaard splittings based on the graph dual to the curve complex and on the pants complex defined by Hatcher and Thurston. As the Heegaard splitting is stabilized, the sequence of complexities turns out to converge to a non-trivial limit depending only on the manifold. We then use a similar method to compare different manifolds, defining a distance which converges under stabilization to an integer related to Dehn surgeries between the two manifolds.

DOI : 10.2140/agt.2006.6.853
Keywords: Heegaard splitting, curve complex, pants complex

Johnson, Jesse  1

1 Mathematics Department, University of California, Davis, CA 95616, USA 
@article{10_2140_agt_2006_6_853,
     author = {Johnson, Jesse},
     title = {Heegaard splittings and the pants complex},
     journal = {Algebraic and Geometric Topology},
     pages = {853--874},
     year = {2006},
     volume = {6},
     number = {2},
     doi = {10.2140/agt.2006.6.853},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.853/}
}
TY  - JOUR
AU  - Johnson, Jesse
TI  - Heegaard splittings and the pants complex
JO  - Algebraic and Geometric Topology
PY  - 2006
SP  - 853
EP  - 874
VL  - 6
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.853/
DO  - 10.2140/agt.2006.6.853
ID  - 10_2140_agt_2006_6_853
ER  - 
%0 Journal Article
%A Johnson, Jesse
%T Heegaard splittings and the pants complex
%J Algebraic and Geometric Topology
%D 2006
%P 853-874
%V 6
%N 2
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.853/
%R 10.2140/agt.2006.6.853
%F 10_2140_agt_2006_6_853
Johnson, Jesse. Heegaard splittings and the pants complex. Algebraic and Geometric Topology, Tome 6 (2006) no. 2, pp. 853-874. doi: 10.2140/agt.2006.6.853

[1] J F Brock, The Weil–Petersson metric and volumes of 3–dimensional hyperbolic convex cores, J. Amer. Math. Soc. 16 (2003) 495

[2] F Costantino, D Thurston, 3–manifolds efficiently bound 4–manifolds, preprint (2005)

[3] A Hatcher, W Thurston, A presentation for the mapping class group of a closed orientable surface, Topology 19 (1980) 221

[4] J Hempel, 3–manifolds as viewed from the curve complex, Topology 40 (2001) 631

[5] T Kobayashi, A construction of 3–manifolds whose homeomorphism classes of Heegaard splittings have polynomial growth, Osaka J. Math. 29 (1992) 653

[6] M Lackenby, The asymptotic behaviour of Heegaard genus, Math. Res. Lett. 11 (2004) 139

[7] H Rubinstein, M Scharlemann, Comparing Heegaard splittings of non-Haken 3–manifolds, Topology 35 (1996) 1005

[8] E Sedgwick, An infinite collection of Heegaard splittings that are equivalent after one stabilization, Math. Ann. 308 (1997) 65

[9] J Souto, personal correspondence (2005)

[10] F Waldhausen, On mappings of handlebodies and of Heegaard splittings, from: "Topology of Manifolds (Georgia, 1969)", Markham, Chicago, Ill. (1970) 205

Cité par Sources :