Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-25T04:39:43.583Z Has data issue: false hasContentIssue false
  • English
  • Français

Topological criteria for schlichtness

Part of: Genetics and population dynamics Analytic continuation

Published online by Cambridge University Press:  03 April 2013

Zach Teitler
Zach Teitler*
Affiliation:
Department of Mathematics, 1910 University Drive, Boise State University, Boise, ID 83725-1555, USA ([email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give two sufficient criteria for schlichtness of envelopes of holomorphy in terms of topology. These are weakened converses of results of Kerner and Royden. Our first criterion generalizes a result of Hammond in dimension 2. Along the way, we also prove a generalization of Royden's theorem.

Keywords

envelope of holomorphyschlichtnesscovering space

MSC classification

Secondary: 32D10: Envelopes of holomorphy
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 2 , June 2013 , pp. 637 - 640
Copyright
Copyright © Edinburgh Mathematical Society 2013

References

1.Fornæss, J. E. and Zame, W. R., Riemann domains and envelopes of holomorphy, Duke Math. J. 50 (1983), 273–283.CrossRefGoogle Scholar
2.Hammond, C., Schlicht envelopes of holomorphy and topology, Math. Z. 266 (2010), 285–288.CrossRefGoogle Scholar
3.Hatcher, A., Algebraic topology (Cambridge University Press, 2002).Google Scholar
4.Jupiter, D., A schlichtness theorem for envelopes of holomorphy, Math. Z. 253 (2006), 623–633.CrossRefGoogle Scholar
5.Kerner, H., Überlagerungen und Holomorphiehüllen, Math. Annalen 144 (1961), 126–134.CrossRefGoogle Scholar
6.Munkres, J. R., Elements of algebraic topology (Addison-Wesley, 1984).Google Scholar
7.Rotman, J. J., An introduction to the theory of groups, 4th edn, Graduate Texts in Mathematics, Volume 148 (Springer, 1995).CrossRefGoogle Scholar
8.Royden, H. L., One-dimensional cohomology in domains of holomorphy, Annals Math. 78 (1963), 197–200.CrossRefGoogle Scholar
9.Stein, K., Überlagerungen holomorph-vollständiger komplexer Räume, Arch. Math. 7 (1956), 354–361.CrossRefGoogle Scholar