본문 바로가기
KERD
논문KCI 등재

Lower Bounds on Boundary Slope Diameters for Montesinos Knots

Kazuhiro Ichihara|Shigeru Mizushima
경북대학교 자연과학대학 수학과|2009.06|Kyungpook Mathematical Journal|제49권 제2호|pp. 321-348

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

diameterboundary slopesMontesinos knot
주제분류수학

초록

In this paper, we give two lower bounds on the diameter of the boundary slope set of a Montesinos knot. One is described in terms of the minimal crossing numbers of the knots, and the other is related to the Euler characteristics of essential surfaces with the maximal/minimal boundary slopes.

Abstract

In this paper, we give two lower bounds on the diameter of the boundary slope set of a Montesinos knot. One is described in terms of the minimal crossing numbers of the knots, and the other is related to the Euler characteristics of essential surfaces with the maximal/minimal boundary slopes.

참고문헌 (12)

  1. R. J. Aumann, "Asphericity of alternating knots", Ann. Math, 64(2), pp.374~392 (1956)
  2. M. Culler, "Bounded, separating, incompressible surfaces in knot manifolds", Invent. Math, 75, pp.537~545 (1984)
  3. M. Culler, "Boundary slopes of knots", Comment. Math. Helv, 74, pp.530~547 (1999)
  4. M. Culler, "Knots with only two strict essential surfaces", Geometry and Topology Monographs, 7, pp.335~430 (2004)
  5. C. Delman, "Alternating knots satisfy property P", Comment. Math. Helv, 74, pp.376~397 (1999)
  6. A. Hatcher, "On the boundary curves of incompressible surfaces", Paci¯c J. Math, 99, pp.373~377 (1982)
  7. A. Hatcher, "Boundary slopes for Montesinos knots", Topology, 28(4), pp.453~480 (1989)
  8. A. Hatcher, "Incompressible surfaces in 2-bridge knot complements", Invent. Math, 79, pp.225~246 (1985)
  9. K. Ichihara, "Bounds on numerical boundary slopes for Montesinos knots", Hiroshima Math. J, 37(2), pp.211~252 (2007)
  10. K. Ichihara, "Crossing number and diameter of boundary slope set of Montesinos knot", Comm. Anal. Geom, 16(3), pp.565~589 (2008)
  11. T. W. Mattman, "2-bridge knot boundary slopes: di- ameter and genus", Osaka J, Math, 45(2), pp.471~489 (2008)
  12. D. Rolfsen, "Knots and Links", Publish or Perish

관련 논문AI추천

Knots with arbitrarily high distance bridge decompositionsKazuhiro Ichihara, Toshio Saito대한수학회 · 대한수학회보2013 · 제50권 제6호Dehn surgeries on middle/hyper doubly Seifert twisted torus knots강성모대한수학회 · 대한수학회보2020 · 제57권 제1호Knots admitting Seifert-fibered surgeries over $S^2$ with four exceptional fibersSungmo Kang대한수학회 · 대한수학회보2015 · 제52권 제1호Sharp-unknotting Number of a Torus KnotTaizo Kanenobu경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제3호The disjoint curve property and bridge surfaces김흥숙, 홍성복대한수학회 · 대한수학회보2009 · 제46권 제5호A lower bound for the genus of self-amalgamation of Heegaard splittingsFengchun Lei, Fengling Li대한수학회 · 대한수학회보2011 · 제48권 제1호

이 간행물의 다른 논문 (16건)

Regularity for Very Weak Solutions of A-Harmonic Equation with WeightGao Hong-ya, Chu Yu-ming, Zhang Yupp. 195-202Some Properties of (Ｙ) Class OperatorsAhmed Bachir, Salah Mecheripp. 203-209Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator Is Cyclic-Ryan ParallelFlorentino Garcia Santos, Juan de Dios Perezpp. 211-219On the Relationship between Zero-sums and Zero-divisors of SemiringsRebeca V. Lewis Lufi, Andrew J. Hetzelpp. 221-233Meromorphic Function Sharing Two Small Functions with Its DerivativeKai Liu, Xiao-guang Qipp. 235-243
원문 보기