Minimal surfaces in manifolds with 𝑆¹ actions and the simple loop conjecture for Seifert fibered spaces

Hass, Joel

doi:10.1090/S0002-9939-1987-0870806-7

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