1998 (Publication #82)
Normal Euler Class and Singularities of Projections for Polyhedral Surfaces in Four-Space (with Ockle Johnson)
Topology, 37, No. 2 (1998) 419-439.
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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.