The entropy formula for the Ricci flow and its geometric applications¶
Perelman, G. (2002). The entropy formula for the Ricci flow and its geometric applications.
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- Topology
- … its supplements, which introduced the fundamental group, established the foundations of homology theory, formulated the Poincaré conjecture (every simply-connected closed 3-manifold is homeomorphic to the 3-sphere — proved by Grigori Perelman in a series of preprints in 2002-2003 using Hamilton's Ricci flow programme
This sourceThe proofs establish Thurston's geometrisation conjecture for closed orientable 3-manifolds and as a corollary Poincaré's conjecture.
- … its supplements, which introduced the fundamental group, established the foundations of homology theory, formulated the Poincaré conjecture (every simply-connected closed 3-manifold is homeomorphic to the 3-sphere — proved by Grigori Perelman in a series of preprints in 2002-2003 using Hamilton's Ricci flow programme
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