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New Approach to the Generalized Poincare Conjecture

New Approach to the Generalized Poincare Conjecture
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摘要 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 Mn be a n-dimensional, connected, simply connected, compact, closed, smooth manifold and there exists a smooth finite triangulation on Mn which is coordinated with the smoothness structure of Mn. If Sn is the n-dimensional sphere then the manifolds Mn and Sn are homemorphic. 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 Mn be a n-dimensional, connected, simply connected, compact, closed, smooth manifold and there exists a smooth finite triangulation on Mn which is coordinated with the smoothness structure of Mn. If Sn is the n-dimensional sphere then the manifolds Mn and Sn are homemorphic.
机构地区 IIT-BSUIR
出处 《Applied Mathematics》 2013年第9期1361-1365,共5页 应用数学(英文)
关键词 Compact SMOOTH Manifolds RIEMANNIAN Metric SMOOTH TRIANGULATION Homotopy-Equivalence Algorithms Compact Smooth Manifolds Riemannian Metric Smooth Triangulation Homotopy-Equivalence Algorithms
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