본문 바로가기
KERD
논문KCI 등재

Representations of $n$-fold Cyclic Branched Coverings of $(1,1)$-knots up to 10 Crossings as Dunwoody Manifolds

이상율|김근영
영남수학회 (Youngnam Mathematical Society)|2022.01|East Asian Mathematical Journal|제38권 제1호|pp. 107-127

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

cyclic branched covering$(11)$-knot1)$-diagramDunwoody manifolddoubly-pointed Heegaard diagram.
주제분류수학

초록

In this paper, we discuss the relationship between doubly-pointed Heegaard diagrams of $(1,1)$-knots in lens spaces and Dunwoody $3$-manifolds, and then give explicit representations of $n$-fold cyclic branched coverings of all $(1,1)$-knots in $S^3$ up to 10 crossings in Rolfsen's knot table as Dunwoody $3$-manifolds.

Abstract

In this paper, we discuss the relationship between doubly-pointed Heegaard diagrams of $(1,1)$-knots in lens spaces and Dunwoody $3$-manifolds, and then give explicit representations of $n$-fold cyclic branched coverings of all $(1,1)$-knots in $S^3$ up to 10 crossings in Rolfsen's knot table as Dunwoody $3$-manifolds.

참고문헌 (15)

  1. H. Aydin, "Torus knots and Dunwoody manifolds", Siberian Math. J, 45(1), pp.1~6 (2004)
  2. S. A. Bleiler, "Two-generator cable knots are tunnel one", Proc. Amer. Math. Soc, 122(4), pp.1285~1287 (1994)
  3. G. Burde, "Knots" (1985), Walter de Gruyter
  4. A. Cattabriga, "All strongly-cyclic branched coverings of (1, 1)-knots are Dunwoody manifolds", J. London Math. Soc, 70(2), pp.512~528 (2004)
  5. H. R. Cho, "Derivations of Schubert normal forms of 2-bridge knots from (1, 1)-diagrams", J. Knot Theory Ramifications, 28(8), pp.1950048~ (2019)
  6. M. J. Dunwoody, "Cyclic presentations and 3-manifolds", Proc. Inter. Conf., Groups-Korea 94, pp.47~55 (1995), Walter de Gruyter
  7. H. Doll, "A genralized bridge number for links in 3-manifolds", Math. Ann, 294(1), pp.701~717 (1992)
  8. L. Grasselli, "Genus one 1-bridge knots and Dunwoody manifolds", Forum Math, 13(3), pp.379~397 (2001)
  9. C. Hayashi, "1-genus 1-bridge splittings for knots", Osaka J. Math, 41(2), pp.371~426 (2004)
  10. G. Kim, "Doubly-pointed Heegaard diagrams of (1, 1)-knots up to 10 cross-ings and (1, 1)-pretzel knots", ~ (2021)
  11. E. Klimenko, "Two-generator discrete subgroups of Isom(H2) containing orientation-reversing elements", Geom. Dedicata, 72, pp.247~282 (1998)
  12. K. Morimoto, "On unknotting tunnels for knots", Math. Ann, 289(1), pp.143~167 (1991)
  13. K. Morimoto, "Identifying tunnel number one knots", J. of the Mathematical Society of Japan, 48(4), pp.667~688 (1996)
  14. Mario Eudave Muoz, "On nonsimple 3-manifolds and 2-handle addition", Topology Appl, 55(2), pp.131~152 (1994)
  15. D. Rolfsen, "Knots and links" (1976), Publish or Perish, Inc

관련 논문AI추천

Heegaard splittings of branched cyclic coverings of connected sums of lens spacesTatyana Kozlovskaya대한수학회 · 대한수학회보2017 · 제54권 제5호On the 2-bridge knots of Dunwoody (1,1)-knots김수환, 김양곡대한수학회 · 대한수학회보2011 · 제48권 제1호CYCLIC BRANCHED COVERS OF ALTERNATING KNOTS AND L-SPACESMasakazu Teragaito대한수학회 · 대한수학회보2015 · 제52권 제4호COMPLEXITY, HEEGAARD DIAGRAMS AND GENERALIZED DUNWOODY MANIFOLDSAlessia Cattabriga, Andrei Vesnin, Michele Mulazzani대한수학회 · 대한수학회지2010 · 제47권 제3호On the Polynomial of the Dunwoody (1, 1)-knots김수환, 김양곡경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2012 · 제52권 제2호Cyclic presentations of groups and cyclicbranched coverings of (1,1)-knotsMichele Mulazzani대한수학회 · 대한수학회보2003 · 제40권 제1호

이 간행물의 다른 논문 (9건)

Ore Extensions over $\sigma$-rigid Rings이양, 한준철, 심효섭pp. 1-12Multiplicity of Positive Solutions to Schr\"odinger-type Positone Problems고은경pp. 13-20Optimal Control for Self-organizing Target Detection Model in the 1D Case유상욱pp. 21-31Existence of Positive Solutions for Generalized Laplacian Problems with a Parameter김찬균pp. 33-41Structure Jacobi Operators of Semi-invarinat Submanifolds in a Complex Space Form II기우항, 김수진pp. 43-63
원문 보기