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New Approach to the Generalized Poincare Conjecture
IIT-BSUIR, Minsk, Belarus
- 1 IIT-BSUIR, Minsk, Belarus
Applied Mathematics·Volume 04 (2013)·Pages 1361–1365·Published 30 August 2013·DOI10.4236/am.2013.49183
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Abstract
Using our proof of the Poincare conjecture in dimension three and the method of mathematical induction a short and transparent proof of the generalized Poincare conjecture (the main theorem below) has been obtained . Main Theorem. Let M n be a n - dimensional , connected , simply connected , compact , closed , smooth manifold and there exists a smooth finite triangulation on M n which is coordinated with the smoothness structure of M n . If S n is the n - dimensional sphere then the manifolds M n and S n are homemorphic .
KeywordsCompact Smooth ManifoldsRiemannian MetricSmooth TriangulationHomotopy-EquivalenceAlgorithms
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