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Complete classifications of exceptional surgeries on Montesinos knots and alternatingknots

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2014/02/21 20:05 International Congress of Mathematicians

1/1 ページ http://www.icm2014.org/mypage/mypage_abs_view.asp?abs_key=gRaYGBazgJszgBi1GBSPgZq6gZi=

Section : 6. Topology

MSC number : 57M50, 57M25

Complete classifications of exceptional surgeries on Montesinos knots and alternating knots

Kazuhiro Ichihara

1

*, In Dae Jong

2

, Hidetoshi Masai

3

1

Department of Mathematics, College of Humanities and Sciences, Nihon University, Japan

2

Department of Mathematics, Kinki University, Japan

3

Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Japan

Contact Information: [email protected]

Abstract

In the talk, we will consider exceptional surgeries on two family of knots in the 3-sphere; Montesinos knots and alternating knots. Actually we will give complete classifications of exceptional surgeries on such knots. For the case of Montesinos knots, based on joint works by the first two authors, the key ingredient is the use of Rassmussen invariant.

The final step for the case of Montesinos knots and the case of alternating knots are achieved by (super-)computer-aided calculations by the first and the last authors.

Keywords : Montesinos knot, alternating knot, exceptional surgery, Seifert fibered surgery

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