Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-09T14:35:13.634Z Has data issue: false hasContentIssue false

ESSENTIAL EQUIVARIANT MAPS AND BORSUK–ULAM THEOREMS

Published online by Cambridge University Press:  01 June 2000

MÓNICA CLAPP
Affiliation:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, 04510 México DF, Mexico; [email protected]
WACŁAW MARZANTOWICZ
Affiliation:
Faculty of Mathematics and Computer Science, A Mickiewicz University, Poznań, Poland; [email protected]
Get access

Abstract

A full characterization is given of those compact Lie groups G with the property that every G-map XX on a finite-dimensional G-complex X of finite orbit type, XG = Ø, is (non-equivariantly) essential. For arbitrary G, conditions are given on the G-space X which guarantee this property. Finally, conditions are given for the non-existence of a G-map XY inducing a homotopy equivalence XGYG on the fixed point sets. These results have applications to critical point theory of almost G-invariant functionals.

Type
Research Article
Copyright
The London Mathematical Society 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)