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New Trends in Intuitive Geometry pp 49–64Cite as

The Topological Transversal Tverberg Theorem Plus Constraints

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Part of the book series: Bolyai Society Mathematical Studies ((BSMS,volume 27))

  • The research by Pavle V. M. Blagojević leading to these results has received funding from DFG via Berlin Mathematical School. Also supported by the grant ON 174024 of the Serbian Ministry of Education and Science. The research by Aleksandra Dimitrijević Blagojević leading to these results has received funding from the grant ON 174024 of the Serbian Ministry of Education and Science. The research by Günter M. Ziegler received funding from DFG via the Research Training Group “Methods for Discrete Structures” and the Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics.”

Abstract

In this paper we use the strength of the constraint method in combination with a generalized Borsuk–Ulam type theorem and a cohomological intersection lemma to show how one can obtain many new topological transversal theorems of Tverberg type. In particular, we derive a topological generalized transversal Van Kampen–Flores theorem and a topological transversal weak colored Tverberg theorem.

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Acknowledgements

We are grateful to Florian Frick and to the referee for very good observations and useful comments.

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Authors and Affiliations

  1. Inst. Math., FU Berlin, Arnimallee 2, 14195, Berlin, Germany

    Pavle V. M. Blagojević & Günter M. Ziegler

  2. Mat. Institut SANU, Knez Mihailova 36, 11001, Beograd, Serbia

    Pavle V. M. Blagojević & Aleksandra S. Dimitrijević Blagojević

Authors
  1. Pavle V. M. Blagojević
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  2. Aleksandra S. Dimitrijević Blagojević
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  3. Günter M. Ziegler
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Corresponding author

Correspondence to Pavle V. M. Blagojević .

Editor information

Editors and Affiliations

  1. MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    Gergely Ambrus

  2. MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    Imre Bárány

  3. MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    Károly J. Böröczky

  4. MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    Gábor Fejes Tóth

  5. MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    János Pach

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© 2018 János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature

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Blagojević, P.V.M., Blagojević, A.S.D., Ziegler, G.M. (2018). The Topological Transversal Tverberg Theorem Plus Constraints. In: Ambrus, G., Bárány, I., Böröczky, K., Fejes Tóth, G., Pach, J. (eds) New Trends in Intuitive Geometry. Bolyai Society Mathematical Studies, vol 27. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-57413-3_3

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