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Bull. Korean Math. Soc. 2020; 57(1): 1-30

Online first article December 9, 2019      Printed January 31, 2020

https://doi.org/10.4134/BKMS.b180230

Copyright © The Korean Mathematical Society.

Dehn surgeries on middle/hyper doubly Seifert twisted torus knots

Sungmo Kang

Chonnam National University

Abstract

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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.

Keywords: Dehn surgery, twisted torus knots, graph manifolds, middle/hyper doubly Seifert knots, R-R diagrams

MSC numbers: Primary 57M25

Supported by: 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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