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 Mnwhich is coordinated with the
smoothness structure of Mn. If Sn is the n-dimensional sphere then the manifolds Mn and Sn are homemorphic.
Cite this paper
A. Ermolits, "New Approach to the Generalized Poincare Conjecture," Applied Mathematics, Vol. 4 No. 9, 2013, pp. 1361-1365. doi: 10.4236/am.2013.49183.
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