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The hull of Rudin's Klein bottle


Author: John T. Anderson
Journal: Proc. Amer. Math. Soc. 140 (2012), 553-560
MSC (2010): Primary 32E20; Secondary 32V40
DOI: https://doi.org/10.1090/S0002-9939-2011-10998-5
Published electronically: June 2, 2011
MathSciNet review: 2846323
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Abstract: In 1981 Walter Rudin exhibited a totally real embedding of the Klein bottle into $ \mathbb{C}^2$. We show that the polynomially convex hull of Rudin's Klein bottle contains an open subset of $ \mathbb{C}^2$. We also describe another totally real Klein bottle in $ \mathbb{C}^2$ whose hull has topological dimension equal to three.


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John T. Anderson
Affiliation: Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, Massachusetts 01610
Email: anderson@mathcs.holycross.edu

DOI: https://doi.org/10.1090/S0002-9939-2011-10998-5
Keywords: Polynomial hull, Klein bottle
Received by editor(s): November 20, 2010
Published electronically: June 2, 2011
Communicated by: Franc Forstneric
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.