The Poincaré Conjecture and Related Statements

2019 ◽  
pp. 623-685
Author(s):  
Valerii N. Berestovskii
Keyword(s):  
Poincare Conjecture

An inverse to the Poincaré conjecture

2001 ◽  
Vol 77 (1) ◽  
pp. 98-106 ◽  
Author(s):  
M. Kreck
Keyword(s):  
Poincare Conjecture

The Development of Topological 4-manifold Theory

2021 ◽  
pp. 295-330
Author(s):  
Mark Powell ◽  
Arunima Ray
Keyword(s):  
Euclidean Space ◽  
Dimensional Euclidean Space ◽  
Smooth Structures ◽  
Normal Bundles ◽  
Exotic Smooth Structures ◽  
Poincare Conjecture ◽  
Manifold Theory ◽  
Simply Connected

The development of topological 4-manifold theory is described in the form of a flowchart showing the interdependence among many key statements in the theory. In particular, the flowchart demonstrates how the theory crucially relies on the constructions in this book, what goes into the work of Quinn on smoothing, normal bundles, and transversality, and what is needed to deduce the famous consequences, such as the classification of closed, simply connected, topological 4-manifolds, the category preserving Poincaré conjecture, and the existence of exotic smooth structures on 4-dimensional Euclidean space. Precise statements of the results, brief indications of some proofs, and extensive references are provided.

Arbeitsgemeinschaft: Ricci Flow and the Poincaré Conjecture

2008 ◽  
pp. 2621-2654
Author(s):  
Klaus Ecker ◽  
Burkhard Wilking
Keyword(s):  
Ricci Flow ◽  
Poincare Conjecture
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