AM  Vol.4 No.9 , September 2013
New Approach to the Generalized Poincare Conjecture
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.


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.
References
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[2]   A. A. Ermolitski, “On a Geometric Black Hole of a Compact Manifold,” Intellectual Archive Journal, Vol. 1, No. 1, 2012, pp. 101-108.

[3]   J. R. Munkres, “Elementary Differential Topology,” Princeton University Press, Princeton, 1966.

[4]   A. A. Ermolitski, “Three-Dimensional Compact Manifold and the Poincare Conjecture,” Intellectual Archive Journal, Vol. 1, No. 4, 2012, pp. 51-62.

[5]   D. B. Fuks and V. A. Rohlin, “Beginner’s Course in Topology/Geometric Chapters,” Nauka, Moscow, 1977.

[6]   M. W. Hirsch, “Differential Topology,” Springer, New York, Heigelberg, Berlin, 1976.

 
 
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