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

 

Normal Euler classes of knotted surfaces
and triple points on projections


Authors: J. Scott Carter and Masahico Saito
Journal: Proc. Amer. Math. Soc. 125 (1997), 617-623
MSC (1991): Primary 57Q45
MathSciNet review: 1372025
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Abstract: We present a new formula relating the normal Euler numbers of embedded surfaces in $4$-space and the number of triple points on their projections into $3$-space. This formula generalizes Banchoff's formula between normal Euler numbers and branch points on the projections.


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Additional Information

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

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/S0002-9939-97-03760-X
PII: S 0002-9939(97)03760-X
Keywords: Knotted surfaces, normal Euler numbers, checker-board coloring, triple points, branch points
Received by editor(s): July 27, 1995
Additional Notes: Presented at the 872nd meeting of the AMS, Tuscaloosa.
Communicated by: Ronald Stern
Article copyright: © Copyright 1997 American Mathematical Society