The coloured Tverberg theorem, extensions and new results

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Abstract

We prove a multiple coloured Tverberg theorem and a balanced coloured Tverbergtheorem, applying different methods, tools and ideas. The proof of the first theorem uses a multiplechessboard complex (as configuration space) and the Eilenberg–Krasnoselskii theory ofdegrees of equivariant maps for non-free group actions. The proof of the second result relies onthe high connectivity of the configuration space, established by using discrete Morse theory.

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About the authors

Duško Joji´c

University of Banja Luka

Email: ducci68@blic.net

Gaiane Yur'evna Panina

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences; Saint Petersburg State University

Email: gaiane-panina@rambler.ru
Doctor of physico-mathematical sciences, no status

Rade T. Živaljević

Mathematical Institute, Serbian Academy of Sciences and Arts

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