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A Homotopical Conner-Raymond Theorem and a Question of Gottlieb

Published online by Cambridge University Press:  20 November 2018

John Oprea
John Oprea*
Affiliation:
Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115
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Abstract

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A homotopy theoretic version is given of the following result of Conner and Raymond: If the circle acts on a space so that the orbit map induces an injection in homology, then the space fibres over the circle with finite structure group. This homotopical analogue is related to recent results pertaining to the effect of the fundamental group's structure on the Euler characteristic. It is also used in the construction of a compact, simple 7-manifold with trivial Gottlieb group which, together with an infinite dimensional example of Ganea, answers a question of Gottlieb.

Keywords

55P9957S99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 2 , 01 June 1990 , pp. 219 - 229
Copyright
Copyright © Canadian Mathematical Society 1990

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