Homotopic Chain Maps Have Equal s-Homology and d-Homology
The homotopy of chain maps on preabelian categories is investigated and the equality of standard homologies and d-homologies of homotopic chain maps is established. As a special case, if X and Y are the same homotopy type, then their nth d-homology R-modules are isomorphic, and if X is a contractibl...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2016/5647548 |
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| author | M. Z. Kazemi-Baneh |
| author_facet | M. Z. Kazemi-Baneh |
| author_sort | M. Z. Kazemi-Baneh |
| collection | DOAJ |
| description | The homotopy of chain maps on preabelian categories is investigated and the equality of standard homologies and d-homologies of homotopic chain maps is established. As a special case, if X and Y are the same homotopy type, then their nth d-homology R-modules are isomorphic, and if X is a contractible space, then its nth d-homology R-modules for n≠0 are trivial. |
| format | Article |
| id | doaj-art-02b6ed701e15496c9d4d59817f1a48a3 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-02b6ed701e15496c9d4d59817f1a48a32025-02-03T01:27:31ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252016-01-01201610.1155/2016/56475485647548Homotopic Chain Maps Have Equal s-Homology and d-HomologyM. Z. Kazemi-Baneh0Department of Mathematics, University of Kurdistan, P.O. Box 416, Sanandaj 66177-15175, IranThe homotopy of chain maps on preabelian categories is investigated and the equality of standard homologies and d-homologies of homotopic chain maps is established. As a special case, if X and Y are the same homotopy type, then their nth d-homology R-modules are isomorphic, and if X is a contractible space, then its nth d-homology R-modules for n≠0 are trivial.http://dx.doi.org/10.1155/2016/5647548 |
| spellingShingle | M. Z. Kazemi-Baneh Homotopic Chain Maps Have Equal s-Homology and d-Homology International Journal of Mathematics and Mathematical Sciences |
| title | Homotopic Chain Maps Have Equal s-Homology and d-Homology |
| title_full | Homotopic Chain Maps Have Equal s-Homology and d-Homology |
| title_fullStr | Homotopic Chain Maps Have Equal s-Homology and d-Homology |
| title_full_unstemmed | Homotopic Chain Maps Have Equal s-Homology and d-Homology |
| title_short | Homotopic Chain Maps Have Equal s-Homology and d-Homology |
| title_sort | homotopic chain maps have equal s homology and d homology |
| url | http://dx.doi.org/10.1155/2016/5647548 |
| work_keys_str_mv | AT mzkazemibaneh homotopicchainmapshaveequalshomologyanddhomology |