Almost normal surfaces in 3-manifolds

Transactions of the American Mathematical Society

Volumn 352, Issue 1, 2000, Pages 171-207

  Stocking, Michelle ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22844456780     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-99-02296-5     Document Type: Article

References (18)

1. J. Birman and H. Hilden, The homeomorphism problem for the 3-sphere, Bull. AMS 79 (1973), no. 5, 1006-1009.MR 47: 7726
2. A. Casson and C. Gordon, Reducing Heegaard splittings, Topology and its Applications 27 (1987).MR89c: 57020
3. C. Frohman, The topological uniqueness of triply periodic minimal surfaces in R3, J. Diff. Geom. 31 (1990), 277-283.MR 92e: 53008
4. D. Gabai, Foliations and the topology of 3-manifolds III, J. Diff. Geom. 26 (1987).MR89a: 57014b
5. W. Haken, Theorie der normalflachen, Acta Math. 105 (1961), 245-375.MR 25: 4519a
6. _, Some results on surfaces in 3-manifolds, Studies in Modern Topology, M.A.A., Prentice-Hall (1968), 34-98.MR 36: 7118
7. J. Hass and A. Thompson, Neon bulbs and the unknotting of arcs in manifolds, J. Knot Theory Ramifications 6 (1997), 235-242.MR 99c: 57043
8. G. Hemion, The classification of knots and 3-dimensional spaces, Oxford University Press, 1992.MR94g: 57015
9. J. Hempel, 3-manifolds, Princeton University Press, 1976.MR54: 3702
10. W. Jaco, Lectures on three-manifold topology, A.M.S., Regional conference series in math, no. 43, 1980.MR81k: 57009
11. W. Jaco and U. Oertel, An algorithm to decide if a 3-manifold is a Haken manifold, Topology 23 (1984), no. 2, 195-209.MR 85j: 57014
12. W. Jaco and J.H. Rubinstein, A piecewise linear theory of minimal surfaces in 3-manifolds, 3. Diff. Geom. 27 (1988), 493-524.
13. S.V. Matveev, Algorithms for the recognition of the three-dimensional sphere (after A. Thompson), Mat. Sb. 186 (1995), 69-84.MR 96g: 57016
14. J. Pitts and J.H. Rubinstein, Eguivariant minimax and minimal surfaces in geometric three-manifolds, Bull. Amer. Math. Soc. 19 (1988), 303-309.MR 90a: 53014
15. J.H. Rubinstein, Polyhedral minimal surfaces, Heegaard splittings and decision problems for 3-dimensional manifolds, Proceedings of the Georgia Topology Conference, AMS/IP Stud. Adv. Math., vol. 21, Amer. Math. Soc., Providence, HI, 1997, pp. 1-20.MR 98f: 57030
16. M. Scharlemann and A. Thompson, Heegaard splittings of (surface) x / are standard, Math. Ann. 295 (1993), 549-564.MR 94b: 57020
17. A. Thompson, Thin position and the recognition problem for the 3-sphere, Math. Research Letter 1 (1994), 613-630.MR 95k: 57015
18. I. Volodin, V. Kusnezov, and A. Fomenko, On a problem of algorithmic recognition of the standard 3-sphere, Usp. Mat. Nauk 29 (1974), no. 5, 71-168, Russian-English Translation in Russian Math. Survey.MR 53: 9219