Skip to main content

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article

Topological criteria for schlichtness

  • Zach Teitler (a1)
Abstract

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.

Copyright
COPYRIGHT: © Edinburgh Mathematical Society 2013
References
Hide All
1.Fornæss, J. E. and Zame, W. R., Riemann domains and envelopes of holomorphy, Duke Math. J. 50 (1983), 273–283.
2.Hammond, C., Schlicht envelopes of holomorphy and topology, Math. Z. 266 (2010), 285–288.
3.Hatcher, A., Algebraic topology (Cambridge University Press, 2002).
4.Jupiter, D., A schlichtness theorem for envelopes of holomorphy, Math. Z. 253 (2006), 623–633.
5.Kerner, H., Überlagerungen und Holomorphiehüllen, Math. Annalen 144 (1961), 126–134.
6.Munkres, J. R., Elements of algebraic topology (Addison-Wesley, 1984).
7.Rotman, J. J., An introduction to the theory of groups, 4th edn, Graduate Texts in Mathematics, Volume 148 (Springer, 1995).
8.Royden, H. L., One-dimensional cohomology in domains of holomorphy, Annals Math. 78 (1963), 197–200.
9.Stein, K., Überlagerungen holomorph-vollständiger komplexer Räume, Arch. Math. 7 (1956), 354–361.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 8 *
Loading metrics...

Abstract views

Total abstract views: 53 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 13th June 2018. This data will be updated every 24 hours.

Cancel
Confirm
×