본문 바로가기
KERD
논문KCI 등재

Klein Bottles and Dehn Filling on a Component of Twocomponent Link Exterior

Nabil Sayari
경북대학교 자연과학대학 수학과|2020.12|Kyungpook Mathematical Journal|제60권 제4호|pp. 831-837|DOI 10.5666/KMJ.2020.60.4.831

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

Klein bottleDehn fillingessential surfaceScharlemann cycle
주제분류수학

초록

Let M be the exterior of a hyperbolic link K ∪ L in a homology 3-sphere Y , such that the linking number lk(K, L) is non-zero. In this note we prove that if γ is a slope in ∂N(L) such that the manifold ML(γ) obtained by γ-Dehn filling along ∂N(L) contains a Klein bottle, then there is a bound on ∆(µ, γ), depending on the genus of K and on lk(K, L).

Abstract

Let M be the exterior of a hyperbolic link K ∪ L in a homology 3-sphere Y , such that the linking number lk(K, L) is non-zero. In this note we prove that if γ is a slope in ∂N(L) such that the manifold ML(γ) obtained by γ-Dehn filling along ∂N(L) contains a Klein bottle, then there is a bound on ∆(µ, γ), depending on the genus of K and on lk(K, L).

참고문헌 (6)

  1. M. Culler, "Dehn surgery on knots", Ann. Math, 125, pp.237~300 (1987)
  2. C. McA. Gordon, "Dehn surgeries on knots creating essential tori, I", Comm. Anal. Geom., 3(3-4), pp.597~644 (1995)
  3. C. Hayashi, "Only single twists on unknots can produce composite knots", Trans. Amer. Math. Soc, 349(11), pp.4465~4479 (1997)
  4. K. Ichihara, "Klein bottle surgery and genera of knots", Pacific J. Math, 210, pp.317~333 (2003)
  5. D. Matignon, "Non-orientable surfaces and Dehn surgeries", Canad. J. Math, 56(5), pp.1022~1033 (2004)
  6. W. Thurston, "Three dimensional manifolds, Kleinian groups and hyperbolic geometry", Bull. Amer. Math. Soc, 6, pp.357~381 (1982)

관련 논문AI추천

Knots in homology lens spaces determined by their complementsKazuhiro Ichihara, Toshio Saito대한수학회 · 대한수학회보2022 · 제59권 제4호Dehn surgeries on middle/hyper doubly Seifert twisted torus knots강성모대한수학회 · 대한수학회보2020 · 제57권 제1호Lower Bounds on Boundary Slope Diameters for Montesinos KnotsKazuhiro Ichihara, Shigeru Mizushima경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제2호COMMON STABILIZATIONS OF HEEGAARD SPLITTINGS OF KNOT EXTERIORS이정훈대한수학회 · 대한수학회지2010 · 제47권 제1호KNOTS IN S³ ADMITTING GRAPH MANIFOLD DEHN SURGERIES강성모대한수학회 · 대한수학회지2014 · 제51권 제6호Knots with arbitrarily high distance bridge decompositionsKazuhiro Ichihara, Toshio Saito대한수학회 · 대한수학회보2013 · 제50권 제6호

이 간행물의 다른 논문 (14건)

Direct Sums of Strongly Lifting ModulesSaboura Dolati Pishhesari, Shahabaddin Ebrahimi Atani, Mehdi Khoramdelpp. 673-682Characterizations of Lie Triple Higher Derivations of Triangular Algebras by Local ActionsMohd Shuaib Akhtar, Aisha Jabeen, Mohammad Ashrafpp. 683-710On n-Amitsur RingsSodnomkhorloo Tumurbat, Baatar Ochirbat, Deolinda I. C. Mendespp. 711-721The Zero-divisor Graph of Zn[X]]박민지, 김은섭, 임정욱pp. 723-729The p-deformed Generalized Humbert Polynomials and Their PropertiesB. I. Dave, Rajesh V. Savaliapp. 731-752
원문 보기