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

DOI:
https://doi.org/10.1090/S0002-9939-00-05479-4

Published electronically:
June 7, 2000

MathSciNet review:
1695171

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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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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:
https://doi.org/10.1090/S0002-9939-00-05479-4

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