본문 바로가기
KERD
논문KCI 등재

Monodromy Groups on Knot Surgery 4-manifolds

윤기헌
경북대학교 자연과학대학 수학과|2013.12|Kyungpook Mathematical Journal|제53권 제4호|pp. 603-614|DOI http://dx.doi.org/10.5666/KMJ.2013.53.4.603

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

knot surgery 4-manifoldLefschetz brationmonodromy group
주제분류수학

초록

In the article we show that nondi eomorphic symplectic 4-manifolds whichadmit marked Lefschetz fibrations can share the same monodromy group. Explicitlywe prove that, for each integer g > 0, every knot surgery 4-manifold in a familyfE(2)K jK is a bered 2-bridge knot of genus g in S3g admits a marked Lefschetz brationstructure which has the same monodromy group.

Abstract

In the article we show that nondi eomorphic symplectic 4-manifolds whichadmit marked Lefschetz fibrations can share the same monodromy group. Explicitlywe prove that, for each integer g > 0, every knot surgery 4-manifold in a familyfE(2)K jK is a bered 2-bridge knot of genus g in S3g admits a marked Lefschetz brationstructure which has the same monodromy group.

참고문헌 (17)

  1. G. Burde, "Knots" (2003), Walter de Gruyter & Co.
  2. R. Fintushel, "Knots, links, and 4-manifolds", Invent. Math, 134(2), pp.363~400 (1998)
  3. R. Fintushel, "Nondi eomorphic symplectic 4-manifolds with the same Seiberg-Witten invariants", Proceedings of the Kirbyfest, pp.103~111 (1999), Geom. Topol.
  4. R. Fintushel, "Families of simply connected 4-manifolds with the same Seiberg-Witten invariants", Topology, 43(6), pp.1449~1467 (2004)
  5. David Gabai, "Pseudo-Anosov maps and surgery on bred 2- bridge knots", Topology Appl, 37(1), pp.93~100 (1990)
  6. R. Gompf, "A new construction of symplectic manifolds", Ann. of Math, 142(3), pp.527~595 (1995)
  7. R. Gompf, "4-manifolds and Kirby calculus" (1999), American Mathematical Society
  8. Y. Gurtas, "Positive Dehn Twist Expressions for some New Involutions in Mapping Class Group", arXiv:math.GT, 2004
  9. A. Kas, "On the handlebody decomposition associated to a Lefschetz fibration", Pacific J. Math, 89(1), pp.89~104 (1980)
  10. A. Kawauchi, "A survey of knot theory" (1996), Birkhauser Verlag
  11. M. Korkmaz, "Noncomplex smooth 4-manifolds with Lefschetz fibrations", IMRN, 3, pp.115~128 (2001)
  12. Y. Matsumoto, "Lefschetz brations of genus two|a topological approach, Topology and Teichmuller spaces (Katinkulta, 1995)", pp.123~148 (1995), World Sci. Publishing
  13. J. Park, "Nonisomorphic Lefschetz brations on knot surgery 4- manifolds", Math. Ann, 345(3), pp.581~597 (2009)
  14. J. Park, "Lefschetz bration structures on knot surgery 4-manifolds", Michigan Math. J, 60(3), pp.525~544 (2011)
  15. "2013", ~
  16. K.-H. Yun, "On the signature of a Lefschetz fibration coming from an involution", Topology Appl, pp.1994~2012 (2006)
  17. K.-H. Yun, "Twisted fiber sums of Fintushel-Stern's knot surgery 4-manifolds", Trans. Amer. Math. Soc, 360(11), pp.5853~5868 (2008)

관련 논문AI추천

Monodromy Maps of Fibered 2-Bridge Knots as Elements in Automorphism Groups of Free GroupsHiroshi Goda, Masaaki Suzuki경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제3호SYMPLECTIC 4-MANIFOLDS VIA SYMPLECTIC SURGERY ON COMPLEX SURFACE SINGULARITIES박희상, Andr´as I. Stipsicz대한수학회 · 대한수학회보2015 · 제52권 제4호Rational homology disk smoothings and Lefschetz fibrations최학호대한수학회 · 대한수학회지2023 · 제60권 제1호SURFACE BUNDLES OVER SURFACES WITH A FIXED SIGNATURE이주아대한수학회 · 대한수학회지2017 · 제54권 제2호KNOTS IN S³ ADMITTING GRAPH MANIFOLD DEHN SURGERIES강성모대한수학회 · 대한수학회지2014 · 제51권 제6호Rational homology balls in 2-handlebodies박희상, 신동수대한수학회 · 대한수학회보2017 · 제54권 제6호

이 간행물의 다른 논문 (13건)

On the Invariance of Primitive Ideals via ϕ-derivations on Banach Algebras정용수pp. 497-505Some New Application of Power Increasing SequencesWaad Sulaimanpp. 507-513On G-invariant Minimal Hypersurfaces with Constant Scalar Curvatures in S5소재업pp. 515-540Zeros and Uniqueness of Difference Polynomials of Meromorphic FunctionsXiaoguang Qi, Jia Doupp. 541-552Some Identities Involving Euler Polynomials Arising from a Non-linear Differential Equation김태균, 임석훈, 정주희, 박진우pp. 553-563
원문 보기