Classification of Rational Homotopy Type for 8-Cohomological Dimension Elliptic Spaces

Mohamed Rachid Hilal, Hassan Lamane, My Ismail Mamouni

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DOI: 10.4236/apm.2012.21004                

Abstract

The different methods used to classify rational homotopy types of manifolds are in general fascinating and various (see [1,7,8]). In this paper we are interested to a particular case, that of simply connected elliptic spaces, denoted X, by discussing its cohomological dimension. Here we will the discuss the case when dimH*( Χ ;Q)=8 and χ(Χ)=0.

Keywords

Rational Homotopy Theory; Elliptic Spaces; Classification; Rational Homotopy Type; Minimal Model of Sullivan

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	G. Bazzoni and V. Mu?z, “Rational Homotopy Type of Nilmanifolds up to Dimension 6,” arXiv: 1001.3860v1, 2010.
[2]	J. B. Friedlander and S. Halperin, “An Arithmetic Characterization of the Rational Homotopy Groups of Certain Spaces,” Inventiones Mathematicae, Vol. 53, No. 2, 1979, pp. 117-133. doi:10.1007/BF01390029
[3]	Y. Felix, S. Halperin and J.-C. Thomas, “Rational Homotopy Theory,” Graduate Texts in Mathematics, Vol. 205, Springer-Verlag, New York, 2001.
[4]	P. Griffiths and J. Morgan, “Rational Homotopy Theory and Differential Forms,” Progress in Mathematics, Birkh?user, Basel, 1981.
[5]	S. Halperin, “Finitness in the minimal models of Sullivan,” Transactions of American Mathematical Society, Vol. 230, 1977, pp. 173-199.
[6]	I. M. James, “Reduced Product Spaces,” Annals of Mathematics, Vol. 62, No. 1, 1955, pp. 170-197. doi:10.2307/2007107
[7]	G. M. L. Powell, “Elliptic Spaces with the Rational Homotopy Type of Spheres,” Bulletin of the Belgian Mathematical Society—Simon Stevin, Vol. 4, No. 2, 1997, pp. 251-263.
[8]	H. Shiga and T. Yamaguchi, “The Set of Rational Homotopy Types with Given Cohomology Algebra,” Homology, Homotopy and Applications, Vol.5, No. 1, 2003, pp. 423- 436.