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

Canceling branch points on projections of surfaces in $ 4$-space


Authors: J. Scott Carter and Masahico Saito
Journal: Proc. Amer. Math. Soc. 116 (1992), 229-237
MSC: Primary 57Q35; Secondary 57Q45
MathSciNet review: 1126191
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Abstract: A surface embedded in $ 4$-space projects to a generic map in $ 3$-space that may have branch points--each contributing $ \pm 1$ to the normal Euler class of the surface. The sign depends on crossing information near the branch point. A pair of oppositely signed branch points are geometrically canceled by an isotopy of the surface in $ 4$-space. In particular, any orientable manifold is isotopic to one that projects without branch points. This last result was originally obtained by Giller. Our methods apply to give a proof of Whitney's theorem.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1126191-0
PII: S 0002-9939(1992)1126191-0
Keywords: Embedded surfaces in $ 4$-space, projections, branch points, normal Euler number
Article copyright: © Copyright 1992 American Mathematical Society