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Notes on braidzel surfaces for links
Author(s):
Takuji
Nakamura
Journal:
Proc. Amer. Math. Soc.
135
(2007),
559-567.
MSC (2000):
Primary 57M25
Posted:
August 28, 2006
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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:
-
- 1.
- M. Hirasawa, The flat genus of links, Kobe J. Math., 127 (1995), 155-159. MR 1391192 (97g:57006)
- 2.
- A. Kawauchi, A survey of knot theory, Birkhäuser-Verlag, Basel, 1996. MR 1417494 (97k:57011)
- 3.
- T. Nakamura, On canonical genus of fibered knot, J. Knot Theory Ramifications, 11 (2002), 341-352. MR 1905689 (2003b:57009)
- 4.
- D. Rolfsen, Knots and links, Mathematics Lecture Series, No. 7, Publish or Perish, Inc., Berkeley, Calif., 1976. MR 0515288 (58:24236)
- 5.
- L. Rudolph, Quasipositive pretzels, Topology Appl. 115 (2001), no.1, 115-123. MR 1840734 (2003a:57016)
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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
DOI:
10.1090/S0002-9939-06-08478-4
PII:
S 0002-9939(06)08478-4
Keywords:
Pretzel surface,
braidzel surface,
braidzel genus,
free genus,
canonical genus
Received by editor(s):
May 4, 2004
Received by editor(s) in revised form:
August 23, 2005
Posted:
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 of article:
Copyright
2006,
American Mathematical Society
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