Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2021; 36(4): 835-840

Online first article December 23, 2020      Printed October 31, 2021

https://doi.org/10.4134/CKMS.c200339

Copyright © The Korean Mathematical Society.

Rationalized evaluation subgroups of the complex Hopf fibration

Oteng Maphane

Botswana International University of Science and Technology

Abstract

In this paper, we compute the rational evaluation subgroup of the Hopf fibration $ S^{2n+1}\hookrightarrow \C P(n). $ We show that, for the Sullivan model $ \phi:A\rightarrow B, $ where $ A $ and $ B $ are the minimal Sullivan models of $ \C P(n) $ and $ S^{2n+1} $ respectively, the evaluation subgroup $ G_{n}(A,B;\phi) $ and the relative evaluation subgroup $ G_{n}^{rel}(A,B;\phi) $ of $ \phi $ are generated by single elements.

Keywords: Evaluation subgroups, Hopf fibration, $G$-sequence

MSC numbers: Primary 55P62; Secondary 54C35

Supported by: This work was completed with the support of the Botswana International University of Science and Tecnnology (BIUST).