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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A combinatorial formula for the normal Euler class of a lattice $ 2$-manifold in $ 4$-space


Author: Boris V. Yusin
Journal: Proc. Amer. Math. Soc. 92 (1984), 578-592
MSC: Primary 57R20; Secondary 52A25, 53A07, 57Q35
MathSciNet review: 760949
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Abstract: For a lattice $ 2$-manifold immersed in $ 4$-space with all faces parallel to coordinate planes it is possible to assign a local index to each vertex type in a unique way so that the sum of vertex indices gives the normal Euler number of the immersion. Related results for simplicial immersions have been established by T. Banchoff.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0760949-8
PII: S 0002-9939(1984)0760949-8
Keywords: Normal curvature, normal Euler class, lattice $ 2$-manifold, curvature for polyhedra, combinatorial formulas for characteristic classes
Article copyright: © Copyright 1984 American Mathematical Society