Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Normal Euler classes of knotted surfaces and triple points on projections

Author(s): J. Scott Carter; 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.

References:

1.: Banchoff, T. F., Double Tangency Theorems for Pairs of Submanifolds, in Geometry Symposium Utrecht 1980 ed. Looijenga, Seirsma, and Takens, LNM v. 894, Springer-Verlag (1981), 26-48. MR 83h:53005
2.: Carter, J. Scott, and Saito, Masahico, Canceling Branch Points on the Projections of Knotted Surfaces in 4-space, Proc. of the AMS. 116, No 1 (Sept 1992), 229-237. MR 93i:57029
3.: Carter, J. Scott, and Saito, Masahico, Reidemeister Moves for Surface Isotopies and Their Interpretation as Moves to Movies, J. of Knot Theory and its Ramifications 2, 251-284. MR 94i:57007
4.: Carter, J. Scott, and Saito, Masahico, -dimensional projections of -manifolds in -space, preprint.
5.: M. Golubitsky, and V. Guillemin, Stable mappings and their singularities, Graduate texts in math. vol. 14, Springer-Verlag, 1973. MR 49:6269
6.: S. E. Cappel and J. L. Shaneson, An introduction to embeddings, immersions and singularities in codimension two, Proc. Sympos. Pure Math. vol. 32, AMS, Providence, RI, 1978. MR 80e:57013
7.: Coghlan, Leslie, Private correspondences.
8.: A. Szücs, Surfaces in $\mathbf {R}^3$ , Bull. London Math. Soc. 18 (1986), 60-66. MR 88a:57060

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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: 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
Copyright of article: Copyright 1997, American Mathematical Society

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