Proceedings of the American Mathematical Society

Author(s): J. Scott Carter; Seiichi Kamada; Masahico Saito
Journal: Proc. Amer. Math. Soc. 128 (2000), 3761-3771.
MSC (2000): Primary 57Q45; Secondary 57R20, 57R42
Posted: June 7, 2000
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A generic projection of a knotted oriented surface in 4-space divides

-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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 57Q45, 57R20, 57R42

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: 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
Posted: 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
Copyright of article: Copyright 2000, American Mathematical Society

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