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Tangential and normal Euler numbers, complex points, and singularities of projections for oriented surfaces in four-space
Mathematics and Computer Science
  • Thomas Banchoff
  • Frank A. Farris, Santa Clara University
Document Type
Publication Date
Mathematical Sciences Publishers
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.
Reprinted with permission by Mathematical Sciences Publishers.
Citation Information
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