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  • 标题:Wecken type problems for self-maps of the Klein bottle
  • 本地全文:下载
  • 作者:D. L. Gonçalves ; M. R. Kelly
  • 期刊名称:Fixed Point Theory and Applications
  • 印刷版ISSN:1687-1820
  • 电子版ISSN:1687-1812
  • 出版年度:2006
  • 卷号:2006
  • DOI:10.1155/FPTA/2006/75848
  • 出版社:Hindawi Publishing Corporation
  • 摘要:

    We consider various problems regarding roots and coincidence points for maps into the Klein bottle K . The root problem where the target is K 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 K to K is established, and we also obtain the following 1-parameter result. Families f n , g : K → K which are coincidence free but any homotopy between f n and f m , n ≠ m , creates a coincidence with g . This is done for any pair of maps such that the Nielsen coincidence number is zero. Finally, we exhibit one such family where g is the constant map and if we allow for homotopies of g , then we can find a coincidence free pair of homotopies.

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