Canceling branch points on projections of surfaces in space
Authors:
J. Scott Carter and Masahico Saito
Journal:
Proc. Amer. Math. Soc. 116 (1992), 229237
MSC:
Primary 57Q35; Secondary 57Q45
MathSciNet review:
1126191
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Abstract: A surface embedded in space projects to a generic map in space that may have branch pointseach contributing 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 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/S00029939199211261910
PII:
S 00029939(1992)11261910
Keywords:
Embedded surfaces in space,
projections,
branch points,
normal Euler number
Article copyright:
© Copyright 1992
American Mathematical Society
