JOURNAL BROWSE
Search
Advanced SearchSearch Tips
DISJOINT PAIRS OF ANNULI AND DISKS FOR HEEGAARD SPLITTINGS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
DISJOINT PAIRS OF ANNULI AND DISKS FOR HEEGAARD SPLITTINGS
SAITO TOSHIO;
  PDF(new window)
 Abstract
We consider interesting conditions, one of which will be called the disjoint property, on genus Heegaard splittings of compact orient able 3-manifolds. Here a Heegaard splitting admits the disjoint property if there are an essential annulus Ai normally embedded in and an essential disk such that is disjoint from . It is proved that all genus Heegaard splittings of toroidal manifolds and Seifert fibered spaces admit the disjoint property.
 Keywords
Heegaard splittings;the disjoint (A,D)-pair property;
 Language
English
 Cited by
1.
THE DISJOINT CURVE PROPERTY AND BRIDGE SURFACES,;;

대한수학회보, 2009. vol.46. 5, pp.1019-1029 crossref(new window)
1.
Parity criterion for unstabilized Heegaard splittings, Mathematical Proceedings of the Cambridge Philosophical Society, 2010, 149, 01, 115  crossref(new windwow)
 References
1.
M. Boileau and J. P. Otal, Groupes des diffeotopies de certaines varietes de Seifert, C. R. Math. Acad. Sci. Paris 303 (1986), 19-22

2.
F. Bonahon and J. P. Otal, Scindements de Heegaard des espaces lenticulaires, Ann. Sci. Ecole. Norm. Sup. 16 (1983), 451-466

3.
A. Casson and C. McA. Gordon, Reducing Heegaard splittings, Topology Appl. 27 (1987), 275-283 crossref(new window)

4.
W. Haken, Studies in Modern Topology, Prentice Hall, 1968

5.
J. Hempel, 3-manifolds as viewed from the curve complex, Topology 40 (2001) 631-657 crossref(new window)

6.
T. Kobayashi, Casson-Gordon's rectangle condition of Heegaard diagrams and in-compressible tori in 3-manifolds, Osaka J. Math. 25 (1988), 553-573

7.
Y. Moriah and J. Schultens, Irreducible Heegaard splittings of Seifert -bered spaces are either vertical or horizontal, Topology 37 (1998), 1089-1112 crossref(new window)

8.
S. Schleimer, The disjoint curve property, Geom. Topol. 8 (2004), 77-113 crossref(new window)

9.
J. Schultens, The Heegaard splittings of Seifert fibered spaces with boundary, Trans.Amer. Math. Soc. 347 (1995), 2533-2552 crossref(new window)

10.
E. Sedgwick, The irreducibility of Heegaard splittings of Seifert fibered spaces Pacific J. Math. 190 (1999), 173-199 crossref(new window)

11.
A. Thompson, The disjoint curve property and genus 2 manifolds, Topology Appl. 97 (1999), 273-279 crossref(new window)