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Bulletin of the London Mathematical Society Advance Access published online on April 23, 2008
Bulletin of the London Mathematical Society, doi:10.1112/blms/bdn020
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© 2008 London Mathematical Society

Seifert surfaces in open books, and a new coding algorithm for links

Rei Furihata

Yosami Junior High School
5-1 Kamizawatari Ogakie-cho
Kariya city
Aichi 448-0813
Japan

Mikami Hirasawa

Department of Mathematics
Nagoya Institute of Technology
Nagoya
Aichi 466-8555
Japan

Tsuyoshi Kobayashi

Department of Mathematics
Nara Women's University
Kitauoya Nishimachi
Nara 630-8506
Japan
tsuyoshi@cc.nara-wu.ac.jp

Received 30 November 2005. Revision received 16 August 2007.

We show that for any link L, there exists a Seifert surface for L that is obtained by successively plumbing flat annuli to a disk D, where the gluing regions are all in D. This furnishes a new way of coding links. We also present an algorithm to read the code directly from a braid presentation.

The second author was partially supported by MEXT,Grant-in-Aid for Young Scientists (B) 1874035, and the third author was partially supported by JSPS, Grant-in-Aid for Scientific Research (C) 17540077.

2000 Mathematics Subject Classification 57M25.


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