Mathematical Research Letters

Volume 25 (2018)

Number 6

Dehn’s Lemma for immersed loops

Pages: 1827 – 1836

DOI: https://dx.doi.org/10.4310/MRL.2018.v25.n6.a6

Authors

Michael Freedman (Microsoft Research Station Q, and Department of Mathematics, University of California at Santa Barbara)

Martin Scharlemann (Department of Mathematics, University of California at Santa Barbara)

Abstract

Suppose $\delta$ is a generic immersed closed curve in the boundary of a $3$-manifold $M$ and $\delta$ is null-homotopic in $M$. Then $\delta$ can be displaced by a height function in a collar of the boundary of $M$ so that the resulting simple closed curve in the collar bounds a disk in $M$.

Received 3 August 2017

Published 25 March 2019