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 |
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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 |
| _version_ | 1818739287748771840 |
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| author | M. R. Kelly D. L. Gonçalves |
| author_facet | M. R. Kelly D. L. Gonçalves |
| author_sort | M. R. Kelly |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-18T01:22:26Z |
| format | Article |
| id | doaj.art-322402d8e4de47508c9d486305b1e9fd |
| institution | Directory Open Access Journal |
| issn | 1687-1820 1687-1812 |
| language | English |
| last_indexed | 2024-12-18T01:22:26Z |
| publishDate | 2006-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Applications |
| spelling | doaj.art-322402d8e4de47508c9d486305b1e9fd2022-12-21T21:25:47ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122006-03-01200610.1155/FPTA/2006/75848Wecken type problems for self-maps of the Klein bottleM. R. KellyD. L. GonçalvesWe 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.http://dx.doi.org/10.1155/FPTA/2006/75848 |
| spellingShingle | M. R. Kelly D. L. Gonçalves Wecken type problems for self-maps of the Klein bottle Fixed Point Theory and Applications |
| title | Wecken type problems for self-maps of the Klein bottle |
| title_full | Wecken type problems for self-maps of the Klein bottle |
| title_fullStr | Wecken type problems for self-maps of the Klein bottle |
| title_full_unstemmed | Wecken type problems for self-maps of the Klein bottle |
| title_short | Wecken type problems for self-maps of the Klein bottle |
| title_sort | wecken type problems for self maps of the klein bottle |
| url | http://dx.doi.org/10.1155/FPTA/2006/75848 |
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