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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Minimal surfaces in manifolds with $ S\sp 1$ actions and the simple loop conjecture for Seifert fibered spaces


Author: Joel Hass
Journal: Proc. Amer. Math. Soc. 99 (1987), 383-388
MSC: Primary 57N10; Secondary 53A10
MathSciNet review: 870806
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Abstract: The Simple Loop Conjecture for $ 3$-manifolds states that if a $ 2$-sided map from a surface to a $ 3$-manifold fails to inject on the fundamental group, then there is an essential simple loop in the kernel. This conjecture is solved in the case where the $ 3$-manifold is Seifert fibered. The techniques are geometric and involve studying least area surfaces and circle actions on Seifert Fibered Spaces.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0870806-7
PII: S 0002-9939(1987)0870806-7
Article copyright: © Copyright 1987 American Mathematical Society