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New Approach to the Generalized Poincare Conjecture

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DOI: 10.4236/am.2013.49183    2,767 Downloads   3,895 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.

Conflicts of Interest

The authors declare no conflicts of interest.

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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