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(76) Normal Euler Class and Singularities of Projections for
Polyhedral Surfaces in Four-Space (with Ockle Johnson)
Topology, 37, No. 2 (1998) 419-439.
View a review at MathSciNet
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.
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