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

 

Titus' homotopies of normal curves


Author: George K. Francis
Journal: Proc. Amer. Math. Soc. 30 (1971), 511-518
MSC: Primary 55.70; Secondary 30.00
MathSciNet review: 0285009
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Abstract: A regular homotopy of a plane immersion of the circle, each of whose stages is a normal curve with the exception of a finite number of stages of the homotopy presenting a nonnegative convex double point self tangency or a transverse triple point, preserves the number of topologically inequivalent extensions of the immersion to an orientation preserving immersion of the disk. Extensions to properly interior mappings of the disk are similarly investigated.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0285009-5
PII: S 0002-9939(1971)0285009-5
Keywords: Branch points, general position, intersection sequence, lifting arcs, light-open maps, monotone homotopy, normal immersions, properly interior maps, regular homotopy, topological equivalence
Article copyright: © Copyright 1971 American Mathematical Society