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

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 dim*H**( Χ ;Q)=8 and χ(*Χ*)=0.

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 dim

Cite this paper

M. Hilal, H. Lamane and M. Mamouni, "Classification of Rational Homotopy Type for 8-Cohomological Dimension Elliptic Spaces,"*Advances in Pure Mathematics*, Vol. 2 No. 1, 2012, pp. 15-21. doi: 10.4236/apm.2012.21004.

M. Hilal, H. Lamane and M. Mamouni, "Classification of Rational Homotopy Type for 8-Cohomological Dimension Elliptic Spaces,"

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.

[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.