论文信息 - The normal Euler class and singularities of projections for polyhedral surfaces in 4-space

The normal Euler class and singularities of projections for polyhedral surfaces in 4-space

Abstract This paper defines the Normal Euler Number and the Normal Euler Class for polyhedral surfaces in 4-space by means of singularities of projections into hyperplanes. There exist polyhedral analogues of nearly all of Whitney's theorems on Normal Euler Classes of surfaces smoothly immersed in 4-space. However, although the Normal Euler Number of a smooth embedding of the real projective plane in 4-space must be plus or minus 2, the Normal Euler Number of a (locally knotted) polyhedral embedding of the real projective plane can be any integer congruent to 2 modulo 4.

Thomas F. Banchoff | T. Banchoff | Ockle Johnson | Ockle Johnson

[1] W. Massey. Proof of a conjecture of Whitney. , 1969 .

[2] Reibun Takase. Note on Orientable Surfaces in 4-Space , 1963 .

[3] Frank A. Farris,et al. Tangential and normal Euler numbers, complex points, and singularities of projections for oriented surfaces in four-space , 1993 .

[4] Normal curvatures and Euler classes for polyhedral surfaces in 4-space , 1984 .

[5] T. Banchoff. Critical Points and Curvature for Embedded Polyhedral Surfaces , 1970 .

[6] N. H. Kuiper. Hyperbolic 4-manifolds and tesselations , 1988 .

[7] G. T. Whyburn,et al. Lectures in topology , 1942 .

[8] Thomas Banchoff,et al. Whitney duality and singularities of projections , 1977 .

[9] H. Whitney. On the Topology of Differentiable Manifolds , 1992 .

[10] Ockle Johnson. Critical point theorems and Whitney duality for polyhedral surfaces , 1994 .

[11] M. Saito,et al. Canceling branch points on projections of surfaces in 4-space , 1992 .

[12] S. Kamada. Nonorientable surfaces in 4-space , 1989 .

[13] H. Whitney. On the Theory of Sphere-Bundles. , 1940, Proceedings of the National Academy of Sciences of the United States of America.

[14] R. Remmert,et al. Perspectives in mathematics : anniversary of Oberwolfach 1984 , 1984 .

[15] W. Thurston,et al. Hyperbolic 4-manifolds and conformally flat 3-manifolds , 1988 .

[16] Thomas Banchoff,et al. Triple points and surgery of immersed surfaces , 1974 .