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http://dx.doi.org/10.4134/BKMS.b170015

A NOTE ON PROOF OF GORDON'S CONJECTURE  

Du, Kun (School of Mathematics and Statistics Lanzhou University)
Publication Information
Bulletin of the Korean Mathematical Society / v.55, no.3, 2018 , pp. 699-715 More about this Journal
Abstract
In this paper, we show a proof of Gordon's Conjecture by using Qiu's labels and two new labels.
Keywords
Heegaard splitting; stabilization; band sum; Gordon's Conjecture;
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1 D. Bachman, Connected sums of unstabilized Heegaard splittings are unstabilized, Geom. Topol. 12 (2008), no. 4, 2327-2378.   DOI
2 R. Kirby, Problems in low dimensional manifold theory, in Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976), Part 2, 273-312, Proc. Sympos. Pure Math., XXXII, Amer. Math. Soc., Providence, RI, 1978.
3 T. Kobayashi and R. Qiu, The amalgamation of high distance Heegaard splittings is always efficient, Math. Ann. 341 (2008), no. 3, 707-715.   DOI
4 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.   DOI
5 M. Lackenby, The Heegaard genus of amalgamated 3-manifolds, Geom. Dedicata 109 (2004), 139-145.   DOI
6 R. Qiu, Stabilizations of reducible Heegaard splittings, arXiv: math. GT/0409497.
7 R. Qiu and M. Scharlemann, A proof of the Gordon conjecture, Adv. Math. 222 (2009), no. 6, 2085-2106.   DOI
8 J. Schultens, The classification of Heegaard splittings for (compact orientable surface) ${\times}S^1$, Proc. London Math. Soc. (3) 67 (1993), no. 2, 425-448.
9 J. Schultens and R. Weidmann, Destabilizing amalgamated Heegaard splittings, in Workshop on Heegaard Splittings, 319-334, Geom. Topol. Monogr., 12, Geom. Topol. Publ., Coventry, 2007.