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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Alexander numbering of knotted surface diagrams


Authors: J. Scott Carter, Seiichi Kamada and Masahico Saito
Journal: Proc. Amer. Math. Soc. 128 (2000), 3761-3771
MSC (2000): Primary 57Q45; Secondary 57R20, 57R42
Published electronically: June 7, 2000
MathSciNet review: 1695171
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Abstract | References | Similar Articles | Additional Information

Abstract:

A generic projection of a knotted oriented surface in 4-space divides $3$-space into regions. The number of times (counted with sign) that a path from infinity to a given region intersects the projected surface is called the Alexander numbering of the region. The Alexander numbering is extended to branch and triple points of the projections. A formula that relates these indices is presented.


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Additional Information

J. Scott Carter
Affiliation: Department of Mathematics, University of South Alabama, Mobile, Alabama 36688
Email: carter@mathstat.usouthal.edu

Seiichi Kamada
Affiliation: Department of Mathematics, Osaka City University, Osaka 558-8585, Japan
Address at time of publication: University of South Alabama, Mobile, Alabama 36688
Email: kamada@sci.osaka-cu.ac.jp

Masahico Saito
Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620
Email: saito@math.usf.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05479-4
PII: S 0002-9939(00)05479-4
Keywords: Knotted surface diagrams, Alexander numbering, triple points, branch points, surface braids
Received by editor(s): November 16, 1998
Received by editor(s) in revised form: March 1, 1999
Published electronically: June 7, 2000
Additional Notes: The second author is supported by a Fellowship from the Japan Society for the Promotion of Science.
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2000 American Mathematical Society