Skip to Main Content

Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Extending closed plane curves to immersions of the disk with $n$ handles
HTML articles powered by AMS MathViewer

by Keith D. Bailey PDF
Trans. Amer. Math. Soc. 206 (1975), 1-24 Request permission

Abstract:

Let $f:S \to E$ be a normal curve in the plane. The extensions of $f$ to immersions of the disk with $n$ handles $({T_n})$ can be determined as follows. A word for $f$ is constructed using the definitions of Blank and Marx and a combinatorial structure, called a ${T_n}$-assemblage, is defined for such words. There is an immersion extending $f$ to ${T_n}$ iff the tangent winding number of $f$ is $1 - 2n$ and $f$ has a ${T_n}$-assemblage. For each $n$, a canonical curve ${f_n}$ with a topologically unique extension to ${T_n}$ is described (${f_0}$ = Jordan curve). Any extendible curve with the minimum number $(2n + 2\;{\text {for}}\;n > 0)$ of self-intersections is equivalent to ${f_n}$.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 57D40
  • Retrieve articles in all journals with MSC: 57D40
Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 206 (1975), 1-24
  • MSC: Primary 57D40
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0370621-3
  • MathSciNet review: 0370621