Tangential and normal Euler numbers, complex points, and singularities of projections for oriented surfaces in four-space

Authors

Thomas Banchoff
Frank A. Farris, Santa Clara UniversityFollow

Document Type

Article

Publication Date

11-1993

Publisher

Mathematical Sciences Publishers

Abstract

For a compact oriented smooth surface immersed in Euclidean four-space (thought of as complex two-space), the sum of the tangential and normal Euler numbers is equal to the algebraic number of points where the tangent plane is a complex line. This follows from the construction of an explicit homology between the zero-chains of complex points and the zero-chains of singular points of projections to lines and hyperplanes representing the tangential and normal Euler classes.

Comments

Reprinted with permission by Mathematical Sciences Publishers. http://doi.org/10.2140/pjm.1993.161.1

Recommended Citation

Banchoff, Thomas, and Frank Farris. "Tangential and Normal Euler Numbers, Complex Points, and Singularities of Projections for Oriented Surfaces in Four-space." Pacific Journal of Mathematics 161.1 (1993): 1-24