참고문헌
- D. Bachman and R. Derby-Talbot, Degeneration of Heegaard genus, a survey, Workshop on Heegaard Splittings, 1-15, Geom. Topol. Monogr., 12, Geom. Topol. Publ., Coventry, 2007.
- D. Bachman, S. Schleimer, and E. Sedgwick, Sweepouts of amalgamated 3-manifolds, Algebr. Geom. Topol. 6 (2006), 171-194. https://doi.org/10.2140/agt.2006.6.171
- A. J. Casson and C. McA Gordon, Reducing Heegaard splittings, Topology Appl. 27 (1987), no. 3, 275-283. https://doi.org/10.1016/0166-8641(87)90092-7
- K. Du, F. Lei, and J. Ma, Distance and self-amalgamation of Heegaard splittings, preprint.
- K. Hartshorn, Heegaard splittings of Haken manifolds have bounded distance, Pacific J. Math. 204 (2002), no. 1, 61-75. https://doi.org/10.2140/pjm.2002.204.61
- J. Hempel, 3-manifolds as viewed from the curve complex, Topology 40 (2001), no. 3, 631-657. https://doi.org/10.1016/S0040-9383(00)00033-1
- T. Kobayashi and R. Qiu, The amalgamation of high distance Heegaard splittings is always efficient, Math. Ann. 341 (2008), no. 3, 707-715. https://doi.org/10.1007/s00208-008-0214-7
- T. Kobayashi, R. Qiu, Y. Rieck, and S. Wang, Separating incompressible surfaces and stabilizations of Heegaard splittings, Math. Proc. Cambridge Philos. Soc. 137 (2004), no. 3, 633-643. https://doi.org/10.1017/S0305004104007790
- M. Lackenby, The Heegaard genus of amalgamated 3-manifolds, Geom. Dedicata 109 (2004), 139-145. https://doi.org/10.1007/s10711-004-6553-y
- T. Li, On the Heegaard splittings of amalgamated 3-manifolds, Workshop on Heegaard Splittings, 157-190, Geom. Topol. Monogr., 12, Geom. Topol. Publ., Coventry, 2007.
- Y. Moriah, On boundary primitive manifolds and a theorem of Casson-Gordon, Topology Appl. 125 (2002), no. 3, 571-579. https://doi.org/10.1016/S0166-8641(01)00303-0
- K. Morimoto, Tunnel number, connected sum and meridional essential surfaces, Topology 39 (2000), no. 3, 469-485. https://doi.org/10.1016/S0040-9383(98)00070-6
- R. Qiu and F. Lei, On the Heegaard genera of 3-manifolds containing non-separating surfaces, Topology and physics, 341-347, Nankai Tracts Math., 12, World Sci. Publ., Hackensack, NJ, 2008.
- M. Scharlemann, Local detection of strongly irreducible Heegaard splittings, Topology Appl. 90 (1998), no. 1-3, 135-147. https://doi.org/10.1016/S0166-8641(97)00184-3
- M. Scharlemann and A. Thompson, Thin position for 3-manifolds, Geometric topology (Haifa, 1992), 231-238, Contemp. Math., 164, Amer. Math. Soc., Providence, RI, 1994.
-
M. Scharlemann and A. Thompson, Heegaard splittings of (surface)
${\times}$ I are standard, Math. Ann. 295 (1993), no. 3, 549-564. https://doi.org/10.1007/BF01444902 - M. Scharlemann and M. Tomova, Alternate Heegaard genus bounds distance, Geom. Topol. 10 (2006), 593-617. https://doi.org/10.2140/gt.2006.10.593
- J. Schultens, Additivity of tunnel number for small knots, Comment. Math. Helv. 75 (2000), no. 3, 353-367. https://doi.org/10.1007/s000140050131
- J. Schultens and R. Weidmann, Destabilizing amalgamated Heegaard splittings, Workshop on Heegaard Splittings, 319-334, Geom. Topol. Monogr., 12, Geom. Topol. Publ., Coventry, 2007.
- J. Souto, Distance in the curve complex and Heegaard genus, preprint.
- G. Yang and F. Lei, On amalgamations of Heegaard splittings with high distance, Proc. Amer. Math. Soc. 137 (2009), no. 2, 723-731. https://doi.org/10.1090/S0002-9939-08-09642-1