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ESSENTIAL EQUIVARIANT MAPS AND BORSUK–ULAM THEOREMS

Published online by Cambridge University Press:  01 June 2000

MÓNICA CLAPP  and
WACŁAW MARZANTOWICZ
MÓNICA CLAPP
Affiliation:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, 04510 México DF, Mexico; mclapp@math.unam.mx
WACŁAW MARZANTOWICZ
Affiliation:
Faculty of Mathematics and Computer Science, A Mickiewicz University, Poznań, Poland; marzan@math.amu.edu.pl
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Abstract

A full characterization is given of those compact Lie groups G with the property that every G-map X→X 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 X→Y inducing a homotopy equivalence XG≃YG on the fixed point sets. These results have applications to critical point theory of almost G-invariant functionals.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 61 , Issue 3 , June 2000 , pp. 950 - 960
Copyright
The London Mathematical Society 2000

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