Wecken type problems for self-maps of the Klein bottle
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2006-03-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://dx.doi.org/10.1155/FPTA/2006/75848 |
| Summary: | 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 fn,g:K→K which are coincidence free but any homotopy between fn and fm, 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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| ISSN: | 1687-1820 1687-1812 |