2015/06/08 by Yuri Shimizu, Shimizu, Yuri
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Point processes and geometric inequalities #math.GM #msc:57N10
paper · pdf · doi:10.48550/arxiv.1506.02919
Found a counterexample of the method in the proof, this paper has been withdrawn by the author
arxiv created 2015/11/10 · arxiv updated 2015/11/11
We consider the operation to crush a subset of a manifold to one-point when the result of the crushing also be a manifold. Then the Poincare conjecture is split to two problems; for any closed orientable 3-manifold which is not homeomorphic to the sphere, one is that this operation preserve simply-connectedness, and another one is that we can get a non-simply connected space by applying the operation. We show these propositions in this paper.