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Knots in Washington XXVII; 3rd Japan-USA Workshop in Knot Theory
January 9-11, 2009
George Washington University
Washington, DC, USA

Organizers
Yoshiyuki Ohyama (TWCU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Alexander Shumakovitch (GWU), Kouki Taniyama (Waseda and GWU), Tatsuya Tsukamoto (Osaka IT), Hao Wu (GWU), Akira Yasuhara (Tokyo GU)

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Braids and Open Book Decompositions
by
Keiko Kawamuro
Rice University, The Institute for Advanced Study
Coauthors: Elena Pavelescu

We construct an immersed surface for a braid in an annulus open book decomposition, which is a generalization of the Bennequin surface for a braid in R3. By resolving the singularities of the immersed surface, we obtain an embedded Seifert surface for the braid. We find a self-linking number formula associated to the surface and prove that it is a generalization of the Bennequin's self-linking formula for a braid in R3. We also prove that our self-linking formula is invariant up to mod k under transversal isotopy of the contact structure compatible with the open book decomposition.

Paper reference: arXiv:0901.0414

Date received: January 3, 2009

Copyright © 2009 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # caxq-62.