Rationalized evaluation subgroups of the complex Hopf fibration
Commun. Korean Math. Soc.
Published online December 23, 2020
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 \mathbb{C} P(n). $ We show that, for the Sullivan model $ \phi:A\rightarrow B, $ where $ A $ and $ B $ are the minimal Sullivan models of $ \mathbb{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, Gottlieb group, $G$-sequence
MSC numbers : Primary 55P62; Secondary 54C35
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