TITLE:
New Approach to the Generalized Poincare Conjecture
AUTHORS:
Alexander A.ki Ermolits
KEYWORDS:
Compact Smooth Manifolds; Riemannian Metric; Smooth Triangulation; Homotopy-Equivalence; Algorithms
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.9,
September
25,
2013
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 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.