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Notes on braidzel surfaces for links

Author: Takuji Nakamura
Journal: Proc. Amer. Math. Soc. 135 (2007), 559-567
MSC (2000): Primary 57M25
Published electronically: August 28, 2006
MathSciNet review: 2255303
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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.

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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

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
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
Article copyright: © Copyright 2006 American Mathematical Society