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

 

Isovariant Borsuk-Ulam results for pseudofree circle actions and their converse


Author: Ikumitsu Nagasaki
Journal: Trans. Amer. Math. Soc. 358 (2006), 743-757
MSC (2000): Primary 55M20; Secondary 57S15, 55M25, 55S35
Published electronically: March 18, 2005
MathSciNet review: 2177039
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Abstract: In this paper we shall study the existence of an $S^1$-isovariant map from a rational homology sphere $M$ with pseudofree action to a representation sphere $SW$. We first show some isovariant Borsuk-Ulam type results. Next we shall consider the converse of those results and show that there exists an $S^1$-isovariant map from $M$ to $SW$ under suitable conditions.


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Additional Information

Ikumitsu Nagasaki
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
Email: nagasaki@math.sci.osaka-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-05-03822-5
PII: S 0002-9947(05)03822-5
Keywords: Isovariant map, Borsuk-Ulam theorem, pseudofree action, multidegree, Hopf theorem, obstruction theory
Received by editor(s): March 1, 2004
Published electronically: March 18, 2005
Additional Notes: The author was partially supported by Grant-in-Aid for Scientific Research.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.