Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Realizability of branched coverings of surfaces

Authors: Allan L. Edmonds, Ravi S. Kulkarni and Robert E. Stong
Journal: Trans. Amer. Math. Soc. 282 (1984), 773-790
MSC: Primary 57M12; Secondary 30F10
MathSciNet review: 732119
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

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

PII: S 0002-9947(1984)0732119-5
Article copyright: © Copyright 1984 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia