Notes on braidzel surfaces for links
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- by Takuji Nakamura PDF
- Proc. Amer. Math. Soc. 135 (2007), 559-567 Request permission
Abstract:
As a generalization of pretzel surfaces, L. Rudolph has introduced a notion of braidzel surfaces in his study of the quasipositivity for pretzel surfaces. In this paper, we show that any oriented link has a braidzel surface. We also introduce a new geometric numerical invariant of links with respect to their braidzel surface and study relationships among them and other “genus” for links.References
- Mikami Hirasawa, The flat genus of links, Kobe J. Math. 12 (1995), no. 2, 155–159. MR 1391192
- Akio Kawauchi, A survey of knot theory, Birkhäuser Verlag, Basel, 1996. Translated and revised from the 1990 Japanese original by the author. MR 1417494
- Takuji Nakamura, On canonical genus of fibered knot, J. Knot Theory Ramifications 11 (2002), no. 3, 341–352. Knots 2000 Korea, Vol. 1 (Yongpyong). MR 1905689, DOI 10.1142/S0218216502001652
- Dale Rolfsen, Knots and links, Mathematics Lecture Series, No. 7, Publish or Perish, Inc., Berkeley, Calif., 1976. MR 0515288
- Lee Rudolph, Quasipositive pretzels, Topology Appl. 115 (2001), no. 1, 115–123. MR 1840734, DOI 10.1016/S0166-8641(00)00051-1
Additional Information
- Takuji Nakamura
- Affiliation: Osaka City University Advanced Mathematical Institute, Sugimoto 3-3-138, Sumiyoshi-ku, Osaka 558-8585, Japan
- Address at time of publication: Research Center for Physics and Mathematics, Faculty of Engineering I, Osaka Electro-Communication University, Hatsucho18-8, Neyagawa, Osaka 572-8530, Japan
- Email: n-takuji@isc.osakac.ac.jp
- Received by editor(s): May 4, 2004
- Received by editor(s) in revised form: August 23, 2005
- Published electronically: August 28, 2006
- Additional Notes: This work was supported by the 21st Century COE program “Constitution of wide-angle mathematical basis focused on knots”.
- Communicated by: Ronald A. Fintushel
- © Copyright 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 559-567
- MSC (2000): Primary 57M25
- DOI: https://doi.org/10.1090/S0002-9939-06-08478-4
- MathSciNet review: 2255303