Poincare's Conjecture for three manifolds
G.S.Makanin
TL;DR
This paper proves Poincare's Conjecture for three-manifolds, establishing that every simply connected, closed three-manifold is topologically a three-sphere, based on Stallings' algebraic formulation.
Contribution
It provides a proof of Poincare's Conjecture for three-manifolds using algebraic methods introduced by Stallings.
Findings
Confirmed Poincare's Conjecture for all simply connected, closed three-manifolds.
Established topological equivalence to the three-sphere for these manifolds.
Utilized algebraic formulation as a key tool in the proof.
Abstract
We prove Poincare's Conjecture that every simply connected, closed three-manifold is topologically equivalent to the three-sphere. The proof is founded on the algebraic formulation discovered by J. Stallings.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Homotopy and Cohomology in Algebraic Topology