New Approach to the Generalized Poincare Conjecture

DOI: 10.4236/am.2013.49183   PDF   HTML     2,956 Downloads   4,308 Views   Citations

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.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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[3] J. R. Munkres, “Elementary Differential Topology,” Princeton University Press, Princeton, 1966.
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[6] M. W. Hirsch, “Differential Topology,” Springer, New York, Heigelberg, Berlin, 1976.

  
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