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Wecken type problems for self-maps of the Klein bottle

Fixed Point Theory and Applications volume 2006, Article number: 75848 (2006) Cite this article

Abstract

We consider various problems regarding roots and coincidence points for maps into the Klein bottle . The root problem where the target is and the domain is a compact surface with non-positive Euler characteristic is studied. Results similar to those when the target is the torus are obtained. The Wecken property for coincidences from to is established, and we also obtain the following 1-parameter result. Families which are coincidence free but any homotopy between and , , creates a coincidence with . This is done for any pair of maps such that the Nielsen coincidence number is zero. Finally, we exhibit one such family where is the constant map and if we allow for homotopies of , then we can find a coincidence free pair of homotopies.

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Authors and Affiliations

  1. Departamento de Matemática, IME-USP, Caixa Postal 66281, Ag. Cidade de São Paulo, São Paulo, SP, 05315-970, Brazil

    DL Gonçalves

  2. Department of Mathematics and Computer Science, Loyola University, 6363 St. Charles Avenue, New Orleans, LA, 70118, USA

    MR Kelly

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  1. DL Gonçalves
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  2. MR Kelly
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Correspondence to MR Kelly.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Gonçalves, D., Kelly, M. Wecken type problems for self-maps of the Klein bottle. Fixed Point Theory Appl 2006, 75848 (2006). https://doi.org/10.1155/FPTA/2006/75848

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