Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 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, $4$-dimensional projections of $3$-manifolds in $5$-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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 57Q45

Retrieve articles in all journals with MSC (1991): 57Q45

Additional Information

J. Scott Carter
Affiliation: Department of Mathematics and Statistics, University of South Alabama, Mobile, Alabama 36688

Masahico Saito
Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620

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

American Mathematical Society