The Michigan Mathematical Journal

Lefschetz fibration structures on knot surgery 4-manifolds

Jongil Park and Ki-Heon Yun

Full-text: Open access

Article information

Source
Michigan Math. J., Volume 60, Issue 3 (2011), 525-544.

Dates
First available in Project Euclid: 8 November 2011

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1320763047

Digital Object Identifier
doi:10.1307/mmj/1320763047

Mathematical Reviews number (MathSciNet)
MR2861087

Zentralblatt MATH identifier
1234.57026

Subjects
Primary: 57N13: Topology of $E^4$ , $4$-manifolds [See also 14Jxx, 32Jxx] 57R17: Symplectic and contact topology 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx]

Citation

Park, Jongil; Yun, Ki-Heon. Lefschetz fibration structures on knot surgery 4-manifolds. Michigan Math. J. 60 (2011), no. 3, 525--544. doi:10.1307/mmj/1320763047. https://projecteuclid.org/euclid.mmj/1320763047


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References

  • M. Akaho, A connected sum of knots and Fintushel–Stern knot surgery on $4$-manifolds, Turkish J. Math. 30 (2006), 87–93.
  • S. Akbulut, Variations on Fintushel–Stern knot surgery on $4$-manifolds, Turkish J. Math. 26 (2002), 81–92.
  • G. Burde and H. Zieschang, Knots, 2nd ed., de Gruyter Stud. Math., 5, de Gruyter, Berlin, 2003.
  • R. Fintushel and R. Stern, Knots, links, and $4$-manifolds, Invent. Math. 134 (1998), 363–400.
  • –––, Constructions of smooth $4$-manifolds, Proceedings of the International Congress of Mathematicians (Berlin, 1998), Doc. Math., Extra Volume II(1998), 443–452.
  • –––, Families of simply connected 4-manifolds with the same Seiberg–Witten invariants, Topology 43 (2004), 1449–1467.
  • GAP Group, GAP–-groups, algorithms, and programming, ver. 4.4.12, 2008.
  • R. Gompf and A. Stipsicz, $4$-manifolds and Kirby calculus, Grad. Stud. Math., 20, Amer. Math. Soc., Providence, RI, 1999.
  • Y. Gurtas, Positive Dehn twist expressions for some new involutions in mapping class group, preprint, 2004, arXiv:math.GT/0404310.
  • J. Harer, How to construct all fibered knots and links, Topology 21 (1982), 263–280.
  • S. Humphries, Generators for the mapping class group, Topology of low-dimensional manifolds (Chelwood Gate, 1977), Lecture Notes in Math., 722, pp. 44–47, Springer-Verlag, Berlin, 1979.
  • –––, Personal e-mail communication.
  • T. Kanenobu, Infinitely many knots with the same polynomial invariant, Proc. Amer. Math. Soc. 97 (1986), 158–162.
  • –––, Examples on polynomial invariants of knots and links, Math. Ann. 275 (1986), 555–572.
  • A. Kas, On the handlebody decomposition associated to a Lefschetz fibration, Pacific J. Math. 89 (1980), 89–104.
  • S. Kinoshita and H. Terasaka, On unions of knots, Osaka J. Math. 9 (1957), 131–153.
  • M. Korkmaz, Noncomplex smooth 4-manifolds with Lefschetz fibrations, Internat. Math. Res. Notices 2001 (2001), 115–128.
  • Y. Matsumoto, Lefschetz fibrations of genus two–-a topological approach, Topology and Teichmüller spaces (Katinkulta, 1995), pp. 123–148, World Scientific, River Edge, NJ.
  • J. Park and K.-H. Yun, Nonisomorphic Lefschetz fibrations on knot surgery $4$-manifolds, Math. Ann. 345 (2009), 581–597.
  • SAGE mathematics software, ver. 3.4, $\langle$http://www.sagemath.org/$\rangle.$
  • J. Stallings, Constructions of fibred knots and links, Algebraic and geometric topology (Stanford, 1976) Proc. Sympos. Pure Math., 32, pp. 55–60, Amer. Math. Soc., Providence, RI, 1978.
  • K.-H. Yun, On the signature of a Lefschetz fibration coming from an involution, Topology Appl. 153 (2006), 1994–2012.
  • –––, Twisted fiber sums of Fintushel–Stern's knot surgery $4$-manifolds, Trans. Amer. Math. Soc. 360 (2008), 5853–5868.