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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Canceling branch points on projections of surfaces in $4$-space
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by J. Scott Carter and Masahico Saito PDF
Proc. Amer. Math. Soc. 116 (1992), 229-237 Request permission

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
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 116 (1992), 229-237
  • MSC: Primary 57Q35; Secondary 57Q45
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1126191-0
  • MathSciNet review: 1126191