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On the 2-bridge knots of Dunwoody (1,1)-knots

김양곡|김수환
대한수학회 (The Korean Mathematical Society)|2011.01|대한수학회보 (Bulletin of the KMS)|제48권 제1호|pp. 197-211

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참고문헌

키워드

crystallizationcyclic branched coveringDunwoody manifold(12-bridge knotHeegaard splitting1)-knot1)-decompositionHeegaard diagramtorus knot
주제분류수학

초록

Every (1,1)-knot is represented by a 4-tuple of integers (a,b, c,r), where a>0, b≥0, c≥0, d=2a+b+c,r ∈ Z_d, and it is well known that all 2-bridge knots and torus knots are (1,1)-knots. In this paper, we describe some conditions for 4-tuples which determine 2-bridge knots and determine all 4-tuples representing any given 2-bridge knot.

Abstract

Every (1,1)-knot is represented by a 4-tuple of integers (a,b, c,r), where a>0, b≥0, c≥0, d=2a+b+c,r ∈ Z_d, and it is well known that all 2-bridge knots and torus knots are (1,1)-knots. In this paper, we describe some conditions for 4-tuples which determine 2-bridge knots and determine all 4-tuples representing any given 2-bridge knot.

참고문헌 (24)

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