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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Minimal surfaces in manifolds with $S^ 1$ actions and the simple loop conjecture for Seifert fibered spaces
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by Joel Hass PDF
Proc. Amer. Math. Soc. 99 (1987), 383-388 Request permission

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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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 99 (1987), 383-388
  • MSC: Primary 57N10; Secondary 53A10
  • DOI: https://doi.org/10.1090/S0002-9939-1987-0870806-7
  • MathSciNet review: 870806