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On topologically minimal surfaces of high genus


Author: Jung Hoon Lee
Journal: Proc. Amer. Math. Soc. 143 (2015), 2725-2730
MSC (2010): Primary 57M50
DOI: https://doi.org/10.1090/S0002-9939-2015-12455-0
Published electronically: January 5, 2015
MathSciNet review: 3326050
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that an irreducible $ 3$-manifold containing an incompressible surface has topologically minimal surfaces of arbitrary high genus.


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  • [1] David Bachman, Critical Heegaard surfaces, Trans. Amer. Math. Soc. 354 (2002), no. 10, 4015-4042 (electronic). MR 1926863 (2003g:57029), https://doi.org/10.1090/S0002-9947-02-03018-0
  • [2] David Bachman, Connected sums of unstabilized Heegaard splittings are unstabilized, Geom. Topol. 12 (2008), no. 4, 2327-2378. MR 2443968 (2009h:57035), https://doi.org/10.2140/gt.2008.12.2327
  • [3] David Bachman, Topological index theory for surfaces in 3-manifolds, Geom. Topol. 14 (2010), no. 1, 585-609. MR 2602846 (2011f:57042), https://doi.org/10.2140/gt.2010.14.585
  • [4] David Bachman, Normalizing topologically minimal surfaces I: Global to local index, arXiv:1210.4573.
  • [5] David Bachman, Normalizing topologically minimal surfaces II: Disks, arXiv:1210.4574.
  • [6] David Bachman, Normalizing topologically minimal surfaces III: Bounded combinatorics, arXiv:1303.6643.
  • [7] David Bachman and Jesse Johnson, On the existence of high index topologically minimal surfaces, Math. Res. Lett. 17 (2010), no. 3, 389-394. MR 2653676 (2011e:57025), https://doi.org/10.4310/MRL.2010.v17.n3.a1
  • [8] Qiang E and Fengchun Lei, Critical Heegaard surfaces obtained by self-amalgamation, J. Knot Theory Ramifications 22 (2013), no. 5, 1350015, 7. MR 3069753, https://doi.org/10.1142/S0218216513500156
  • [9] Jung Hoon Lee, Critical Heegaard surfaces obtained by amalgamation, Topology Appl. 160 (2013), no. 1, 111-116. MR 2995082, https://doi.org/10.1016/j.topol.2012.10.002

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Additional Information

Jung Hoon Lee
Affiliation: Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju 561-756, Korea
Email: junghoon@jbnu.ac.kr

DOI: https://doi.org/10.1090/S0002-9939-2015-12455-0
Keywords: topologically minimal surface, topological index, disk complex, incompressible surface
Received by editor(s): July 24, 2013
Received by editor(s) in revised form: January 6, 2014
Published electronically: January 5, 2015
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2015 American Mathematical Society

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