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Comparing Heegaard splittings – the bounded case. (English) Zbl 0892.57009
The authors generalize their results in [Topology 35, No. 4, 1005-1026 (1996; Zbl 0858.57020)] to 3-manifolds with boundary.

##### MSC:
 57N10 Topology of general $$3$$-manifolds (MSC2010) 57M50 General geometric structures on low-dimensional manifolds
##### Keywords:
Heegaard splitting; genus; bounded
Full Text:
##### References:
 [1] A. J. Casson and C. McA. Gordon, Reducing Heegaard splittings, Topology Appl. 27 (1987), no. 3, 275 – 283. · Zbl 0632.57010 · doi:10.1016/0166-8641(87)90092-7 · doi.org [2] Jean Cerf, Sur les difféomorphismes de la sphère de dimension trois (\Gamma $$_{4}$$=0), Lecture Notes in Mathematics, No. 53, Springer-Verlag, Berlin-New York, 1968 (French). · Zbl 0164.24502 [3] Charles Frohman, Minimal surfaces and Heegaard splittings of the three-torus, Pacific J. Math. 124 (1986), no. 1, 119 – 130. · Zbl 0604.57006 [4] Wolfgang Haken, Some results on surfaces in 3-manifolds, Studies in Modern Topology, Math. Assoc. Amer. (distributed by Prentice-Hall, Englewood Cliffs, N.J.), 1968, pp. 39 – 98. [5] K. Johannson, Topology and Combinatorics of 3-Manifolds, Lecture Notes in Math, 1599 Springer-Verlag, Berlin and New York, 1995. CMP 97:09 · Zbl 0820.57001 [6] H. Rubinstein and M. Scharlemann, Comparing Heegaard splittings of non-Haken 3-manifolds, Topology 35 (1996), 1005-1026. CMP 96:17 · Zbl 0858.57020 [7] H. Rubinstein and M. Scharlemann, Transverse Heegaard splittings, Michigan Math. J. 49 (1997), 69-83. CMP 97:10 · Zbl 0907.57013 [8] J. Schultens, The stabilization problem for Heegaard splittings of Seifert fibered spaces, Topology and its Applications 73(1996), 133-139. CMP 97:03 · Zbl 0867.57013 [10] Martin Scharlemann and Abigail Thompson, Thin position for 3-manifolds, Geometric topology (Haifa, 1992) Contemp. Math., vol. 164, Amer. Math. Soc., Providence, RI, 1994, pp. 231 – 238. · Zbl 0818.57013 · doi:10.1090/conm/164/01596 · doi.org [11] Friedhelm Waldhausen, Heegaard-Zerlegungen der 3-Sphäre, Topology 7 (1968), 195 – 203 (German). · Zbl 0157.54501 · doi:10.1016/0040-9383(68)90027-X · doi.org
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