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Journal of the London Mathematical Society 2004 69(1):214-230; doi:10.1112/S0024610703004721
© 2004 by London Mathematical Society
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© The London Mathematical Society

The Unstable Equivariant Fixed Point Index and the Equivariant Degree

Waclaw Marzantowicz and Carlos Prieto

Faculty of Mathematics and Computer Science, UAM Poznan, Poland, marzan{at}main.amu.edu.pl
Instituto de Matemáticas, UNAM 04510 México, DF, Mexico, cprieto{at}math.unam.mx

Received 13 January 2003. Revision received 16 April 2003.

A correspondence between the equivariant degree introduced by Ize, Massabó, and Vignoli and an unstable version of the equivariant fixed point index defined by Prieto and Ulrich is shown. With the help of conormal maps and properties of the unstable index, a sum decomposition formula is proved for the index and consequently also for the degree. As an application, equivariant homotopy groups are decomposed as direct sums of smaller groups of fixed orbit types, and a geometric interpretation of each summand is given in terms of conormal maps.


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