In year 2019 Wikipedia writes on G. Perelman's proof of Poincare Conjecture: "... he wanted to cut the manifold at the singularities and paste in caps (NB! PROBLEM A), and then run the Ricci (NB! PROBLEM D) flow again... This deforms the manifold into round pieces with strands (NB! PROBLEM B) running between them. He cuts the strands and continues deforming the manifold until eventually he is left with a collection of round three-dimensional spheres. Then he rebuilds the original manifold by connecting the spheres together with three-dimensional cylinders (NB! PROBLEM C), morphs them into a round shape and sees that, despite all the initial confusion, the manifold was in fact homeomorphic to a sphere S. ''
PROBLEM A: the caps, which do not belong to the original manifold M, are going into the final sphere S. These caps K are not present in initial manifold M. And their size is not exactly zero, neither it becomes zero. Thus, holds M+K = Final Sphere. Thus, M is not identical to final sphere. Thus, there is no homeomorphism.
PROBLEM B: the strands, which belong to the original manifold M, are not going into the final sphere S.
PROBLEM C: the cylinders, which do not belong to the original manifold M, are going into the final sphere S.
PROBLEM D: it is not sufficient to demand non-singularity of Ricci Scalar, we need to keep non-singularity of Riemann Curvature Tensor.
The Poincare Conjecture: trivially connected 3D space without edge is homeomorphic to 3D sphere. The word "homeomorphic" means, that by non-singular deformation of initial space, one produces perfect sphere. But pasting in caps, cutting out strands, will not make such deformation.
Copyright: M.Sci. Dmitri Martila, 1.June.2019.
Please comment this too: Is it really Fermat's Last Theorem proven?
PROBLEM A: the caps, which do not belong to the original manifold M, are going into the final sphere S. These caps K are not present in initial manifold M. And their size is not exactly zero, neither it becomes zero. Thus, holds M+K = Final Sphere. Thus, M is not identical to final sphere. Thus, there is no homeomorphism.
PROBLEM B: the strands, which belong to the original manifold M, are not going into the final sphere S.
PROBLEM C: the cylinders, which do not belong to the original manifold M, are going into the final sphere S.
PROBLEM D: it is not sufficient to demand non-singularity of Ricci Scalar, we need to keep non-singularity of Riemann Curvature Tensor.
The Poincare Conjecture: trivially connected 3D space without edge is homeomorphic to 3D sphere. The word "homeomorphic" means, that by non-singular deformation of initial space, one produces perfect sphere. But pasting in caps, cutting out strands, will not make such deformation.
Copyright: M.Sci. Dmitri Martila, 1.June.2019.
Please comment this too: Is it really Fermat's Last Theorem proven?
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