New Approach to the Generalized Poincare Conjecture

• 作者: Alexander A.ki Ermolits
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Compact SMOOTH MANIFOLDS RIEMANNIAN Metric SMOOTH TRIANGULATION Homotopy-Equivalence Algorithms
• 年，卷（期）: 2013,（9）
• 页码范围: 1361-1365
• 页数: 5页
• 分类号: O1

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.