This forum is a combination of the series Guard Dog, and Tsukikage. Shared by: ZHzero and ZHDarigan
 
HomeCalendarFAQSearchMemberlistUsergroupsRegisterLog in

Share | 
 

 Generalized Poincaré conjecture

Go down 
AuthorMessage
kosovohp01



Posts : 714
Join date : 2010-08-26

PostSubject: Generalized Poincaré conjecture   Mon Dec 13, 2010 11:25 pm

In the mathematical area of topology, the term Generalized Poincaré conjecture refers to a statement that a manifold which is a homotopy sphere 'is' a sphere. More precisely, one fixes a category of manifolds: topological (Top), differentiable (Diff), or piecewise linear (PL). Then the statement is
Every homotopy sphere (a closed n-manifold which is homotopy equivalent to the n-sphere) is isomorphic to the n-sphere in the chosen category, i.e. homeomorphic, diffeomorphic, or PL-isomorphic.
The name derives from the Poincaré conjecture, which was made for (topological or PL) manifolds of dimension 3, where being a homotopy sphere is equivalent to being simply connected. The Generalized Poincaré conjecture is known to be true or false in a number of instances, due to the work of many distinguished topologists, including the Fields medal recipients John Milnor, Steve Smale, Michael Freedman and Grigori Perelman.[1

Bahamas Shark Fishing
r4i
Back to top Go down
View user profile
 
Generalized Poincaré conjecture
Back to top 
Page 1 of 1

Permissions in this forum:You cannot reply to topics in this forum
Guard Dog & Tsukikage :: Chill and Chat-
Jump to: