Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48 .

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.

 

Realizability of branched coverings of surfaces
HTML articles powered by AMS MathViewer

by Allan L. Edmonds, Ravi S. Kulkarni and Robert E. Stong PDF
Trans. Amer. Math. Soc. 282 (1984), 773-790 Request permission

Abstract:

A branched covering $M \to N$ of degree $d$ between closed surfaces determines a collection $\mathfrak {D}$ of partitions of $d$—its "branch data"—corresponding to the set of branch points. The collection of partitions must satisfy certain obvious conditions implied by the Riemann-Hurwitz formula. This paper investigates the extent to which any such finite collection $\mathfrak {D}$ of partitions of $d$ can be realized as the branch data of a suitable branched covering. If $N$ is not the $2$-sphere, such data can always be realized. If $\mathfrak {D}$ contains sufficiently many elements compared to $d$, then it can be realized. And whenever $d$ is nonprime, examples are constructed of nonrealizable data.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 57M12, 30F10
  • Retrieve articles in all journals with MSC: 57M12, 30F10
Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 282 (1984), 773-790
  • MSC: Primary 57M12; Secondary 30F10
  • DOI: https://doi.org/10.1090/S0002-9947-1984-0732119-5
  • MathSciNet review: 732119