Open Access

Wecken type problems for self-maps of the Klein bottle

Fixed Point Theory and Applications20062006:75848

https://doi.org/10.1155/FPTA/2006/75848

Received: 6 October 2004

Accepted: 21 July 2005

Published: 16 March 2006

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’ Affiliations

(1)
Departamento de Matemática, IME-USP
(2)
Department of Mathematics and Computer Science, Loyola University

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Copyright

© D. L. Gonc¸alves and M. R. Kelly. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.