Dehn’s lemma and the loop theorem. (English) Zbl 1056.57013

Li, Benghe (ed.) et al., Low dimensional topology. Lectures presented during the program on low-dimensional topology held at the Morningside Center of Mathematics, Beijing, China, 1998/1999. Somerville, MA: International Press (ISBN 1-57146-112-4/pbk). New Stud. Adv. Math. 3, 61-68 (2003).
The article contains a concise, elementary and self-contained introduction to normal surfaces in triangulated 3-manifolds with the fundamental Haken results. A proof of Dehn’s Lemma and the loop theorem is then given along the lines of K. Johannson [Lect. Notes Geom. Topol. 3, 47–54 (1994; Zbl 0862.57006)]. The general idea is explained without working out the details.
For the entire collection see [Zbl 1034.57002].


57M35 Dehn’s lemma, sphere theorem, loop theorem, asphericity (MSC2010)


Zbl 0862.57006