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A short treatise on the equivariant degree theory and its applications

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Abstract

The aim of this survey is to give a profound introduction to equivariant degree theory, avoiding as far as possible technical details and highly theoretical background. We describe the equivariant degree and its relation to the Brouwer degree for several classes of symmetry groups, including also the equivariant gradient degree, and particularly emphasizing the algebraic, analytical, and topological tools for its effective calculation, the latter being illustrated by six concrete examples. The paper concludes with a brief sketch of the construction and interpretation of the equivariant degree.

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Authors and Affiliations

  1. Department of Mathematics and Computer Sciences, Netanya Academic College, Netanya, 42365, Israel

    Zalman Balanov

  2. Department of Mathematical Sciences, University of Texas in Dallas, EC 35, 800 West Campbell Road, Richardson, TX, 75080-3021, USA

    Zalman Balanov & Wieslaw Krawcewicz

  3. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, PL-87-100, Toruń, Poland

    Sławomir Rybicki

  4. Mathematisches Institut, Universität München, Theresienstr. 39, D-80333, München, Germany

    Heinrich Steinlein

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  1. Zalman Balanov
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  2. Wieslaw Krawcewicz
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  3. Sławomir Rybicki
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  4. Heinrich Steinlein
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Balanov, Z., Krawcewicz, W., Rybicki, S. et al. A short treatise on the equivariant degree theory and its applications. J. Fixed Point Theory Appl. 8, 1–74 (2010). https://doi.org/10.1007/s11784-010-0033-9

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