
#1
Sep2210, 06:44 AM

Sci Advisor
HW Helper
PF Gold
P: 4,768

In Lee's Intro to topological manifolds, p.105, it is written that every manifold of dimension 3 or below is triangulable. But in dimension 4, threre are known examples of non triangulable manifolds. In dimensions greater than four, the answer is unknown.
But in BottTu p.190, it is written that every manifold admits a triangulation. Which is right? 



#2
Sep2210, 07:20 AM

Sci Advisor
P: 1,716





#3
Sep2210, 07:32 AM

P: 336

It seems that the authors probably have different definitions of triangulation.
In my opinion, the problem boils down to whether every interval isomorphic to some interval in R^n is triangulable & hence the second statement looks good. 



#4
Sep2210, 07:58 AM

Sci Advisor
P: 1,716

Is every manifold triangulable?Bull. Amer. Math. Soc., 75 (1969), 742749. This paper is said to have an example of a nontriangulable 6 manifold 



#5
Sep2310, 11:24 PM

Sci Advisor
HW Helper
P: 9,421

it seems indeed to depend on your definition of triangulation. in gneral the answer may be unknown.
consult: the history of topology by ioan mackenzie (or ask ron stern) http://books.google.com/books?id=7iR...ble%3F&f=false 


Register to reply 
Related Discussions  
Manifold ?!  Differential Equations  4  
manifold and metric  General Astronomy  2  
O(3) a 3manifold in R^9  Calculus  4  
Hybrid Manifold  Beyond the Standard Model  0  
Hybrid Manifold  Beyond the Standard Model  0 