Poincare conjecture?

  • Thread starter pivoxa15
  • Start date
  • #1
2,255
1
Does the Poincare conjecture say:

Consider a compact 3-dimensional manifold V without boundary.

Poincare conjectured that
The fundamental group of V is trivial => V is homeomorphic to the 3-dimensional sphere?

It has been proved for all manifolds except 3. However Perelman completed a proof that is almost certainly right for 3-manifolds, thereby proving Poincare to be right.

My question is which fundamental group(s) does the statement refer to? i.e denoting pi for the fundamental group, pi_1 consists of 1 dimensional loops. pi_2 consists of 2-D strips...
 
Last edited:

Answers and Replies

  • #2
mathwonk
Science Advisor
Homework Helper
11,012
1,212
fundamental group always means pi1 not pi2.
 
  • #3
2,255
1
right. Have I stated the conjecture correctly?
 

Related Threads on Poincare conjecture?

  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
13
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
2
Views
2K
Replies
6
Views
4K
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
2K
Top