Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-05T16:51:41.661Z Has data issue: false hasContentIssue false

On distinguishing spaces not homotopy-equivalent

Published online by Cambridge University Press:  17 April 2009

M.H. Eggar
Affiliation:
Department of Mathematics and Statistics, The University of Edinburgh, Edinburgh EH9 3JZ, Scotland
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A non-pathological example is given of two topological spaces which have isomorphic homotopy groups, homology groups and cohomology ring and which cannot be distinguished from each other by the Whitehead product structure. A family of examples can be constructed likewise.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Ganea, T., ‘A generalization of the homology and homotopy suspension’, Comm. Math. Helv. 39 (1964), 295322.CrossRefGoogle Scholar
[2]Gray, B.I., ‘Spaces of the same n−type, for all n’, Topology 5 (1966), 241243.CrossRefGoogle Scholar
[3]James, I.M. and Whitehead, J.H.C., ‘Homotopy theory of sphere bundles over spheres’, Proc. London Math. Soc. 4 (1954), 196218.CrossRefGoogle Scholar
[4]Spanier, E.H., Algebraic topology (McGraw Hill, New York, 1969), pp. 99.Google Scholar