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The Unstable Equivariant Fixed Point Index and the Equivariant Degree
Author(s) -
Marzantowicz Wacław,
Prieto Carlos
Publication year - 2004
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610703004721
Subject(s) - equivariant map , mathematics , degree (music) , pure mathematics , fixed point index , interpretation (philosophy) , fixed point , index (typography) , orbit (dynamics) , homotopy , mathematical analysis , physics , computer science , engineering , world wide web , acoustics , programming language , boundary value problem , aerospace engineering
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.