PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (232)
Orphanage
Unclass'd
Unproven (519)
Corrections (23)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: Medium Entry average rating: No information on entry rating
Dehn's lemma (Theorem)

The Dehn's lemma states that if a continuous map from a 2-disk to a 3-manifold $ f\colon D^2\to M$ for which $ f^{-1}f\partial D^2=D^2$, then there exists an embedding $ g\colon D^2\to M$ such that the restrictions $ g\vert\partial$ and $ f\vert\partial$ are equal.



"Dehn's lemma" is owned by juanman.
(view preamble | get metadata)

View style:

See Also: 3-manifold

Other names:  Dehn's lemma
Log in to rate this entry.
(view current ratings)

Cross-references: restrictions, embedding, 3-manifold, continuous map
There are 2 references to this entry.

This is version 8 of Dehn's lemma, born on 2006-03-11, modified 2007-06-24.
Object id is 7713, canonical name is DehnsLemma.
Accessed 1732 times total.

Classification:
AMS MSC: 57M35 (Manifolds and cell complexes :: Low-dimensional topology :: Dehn's lemma, sphere theorem, loop theorem, asphericity)
Pending Errata and Addenda
None.
[ View all 7 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | prove | add result | add corollary | add example | add (any)