[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c200339

RATIONALIZED EVALUATION SUBGROUPS OF THE COMPLEX HOPF FIBRATION

Maphane, Oteng (Department of Mathematics and Statistical Sciemces Botswana International University of Science and Technology)

Publication Information

Communications of the Korean Mathematical Society / v.36, no.4, 2021 , pp. 835-840 More about this Journal

Abstract

In this paper, we compute the rational evaluation subgroup of the Hopf fibration S²ⁿ⁺¹ ↪ ℂP(n). We show that, for the Sullivan model 𝜙 : A → B, where A and B are the minimal Sullivan models of ℂP(n) and S²ⁿ⁺¹ respectively, the evaluation subgroup G_n(A, B; 𝜙) and the relative evaluation subgroup G^rel_n (A, B; 𝜙) of 𝜙 are generated by single elements.

Keywords

Evaluation subgroups; Hopf fibration; G-sequence;

Citations & Related Records

Reference

1	Y. Felix, J. Oprea, and D. Tanre, Algebraic Models in Geometry, Oxford Graduate Texts in Mathematics, 17, Oxford University Press, Oxford, 2008.
2	Y. Felix, S. Halperin, and J.-C. Thomas, Rational Homotopy Theory, Graduate Texts in Mathematics, 205, Springer-Verlag, New York, 2001. https://doi.org/10.1007/978-1-4613-0105-9 DOI
3	D. Sullivan, Infinitesimal computations in topology, Inst. Hautes Etudes Sci. Publ. Math. No. 47 (1977), 269-331 (1978). DOI
4	M. H. Woo and K. Y. Lee, On the relative evaluation subgroups of a CW-pair, J. Korean Math. Soc. 25 (1988), no. 1, 149-160.
5	I. Biswas, M. Fernandez, V. Munoz, and A. Tralle, On formality of Sasakian manifolds, J. Topol. 9 (2016), no. 1, 161-180. https://doi.org/10.1112/jtopol/jtv044 DOI
6	D. H. Gottlieb, Evaluation subgroups of homotopy groups, Amer. J. Math. 91 (1969), 729-756. https://doi.org/10.2307/2373349 DOI
7	G. Lupton and S. B. Smith, Rationalized evaluation subgroups of a map. I. Sullivan models, derivations and G-sequences, J. Pure Appl. Algebra 209 (2007), no. 1, 159-171. https://doi.org/10.1016/j.jpaa.2006.05.018 DOI
8	E. H. Spanier, Algebraic Topology, corrected reprint of the 1966 original, Springer-Verlag, New York, 1989.