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Essential surfaces of non-negative Euler characteristic in genus two handlebody exteriors


Authors: Yuya Koda and Makoto Ozawa; with an appendix by Cameron Gordon
Journal: Trans. Amer. Math. Soc. 367 (2015), 2875-2904
MSC (2010): Primary 57M25; Secondary 57M15
DOI: https://doi.org/10.1090/S0002-9947-2014-06199-0
Published electronically: October 3, 2014
MathSciNet review: 3301885
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Abstract: We provide a classification of the essential surfaces of non-negative Euler characteristic in the exteriors of genus two handlebodies embedded in the 3-sphere.


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Additional Information

Yuya Koda
Affiliation: Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan
Email: koda@math.tohoku.ac.jp

Makoto Ozawa
Affiliation: Department of Natural Sciences, Faculty of Arts and Sciences, Komazawa University, 1-23-1 Komazawa, Setagaya-ku, Tokyo, 154-8525, Japan
Email: w3c@komazawa-u.ac.jp

Cameron Gordon
Affiliation: Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712
Email: gordon@math.utexas.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-06199-0
Keywords: Knot, handlebody, essential surface
Received by editor(s): February 21, 2013
Received by editor(s) in revised form: May 29, 2013
Published electronically: October 3, 2014
Additional Notes: The first-named author was supported in part by Grant-in-Aid for Young Scientists (B) (No. 26800028), Japan Society for the Promotion of Science, and by JSPS Postdoctoral Fellowships for Research Abroad
The second-named author was supported in part by Grant-in-Aid for Scientific Research (C) (No. 23540105), Japan Society for the Promotion of Science.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.