Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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DEHN SURGERIES ON MIDDLE/HYPER DOUBLY SEIFERT TWISTED TORUS KNOTS

  • Kang, Sungmo (Department of Mathematics Education Chonnam National University)
  • Received : 2018.03.14
  • Accepted : 2019.11.07
  • Published : 2020.01.31
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Abstract

In this paper, we classify all twisted torus knots which are middle/hyper doubly Seifert. By the definition of middle/hyper doubly Seifert knots, these knots admit Dehn surgery yielding either Seifert-fibered spaces or graph manifolds at a surface slope. We show that middle/hyper doubly Seifert twisted torus knots admit the latter, that is, non-Seifert-fibered graph manifolds whose decomposing pieces consist of two Seifert-fibered spaces over the disk with two exceptional fibers.

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

The author would like to thank the referees for pointing out errors in the original texts and valuable comments and suggestions. This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (NRF-2017R1D1A1B03029935).

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