On Relative Homotopy Groups of Modules
In his book “Homotopy Theory and Duality,” Peter Hilton described the concepts of relative homotopy theory in module theory. We study in this paper the possibility of parallel concepts of fibration and cofibration in module theory, analogous to the existing theorems in algebraic topology. First, we...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/27626 |
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| _version_ | 1850105968156737536 |
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| author | C. Joanna Su |
| author_facet | C. Joanna Su |
| author_sort | C. Joanna Su |
| collection | DOAJ |
| description | In his book “Homotopy Theory and Duality,” Peter Hilton described the concepts of relative homotopy theory in module theory. We study in this paper the possibility of parallel concepts of fibration and cofibration in module theory, analogous to the existing theorems in algebraic topology. First, we discover that one can study relative homotopy groups, of modules, from a viewpoint which is closer to that of (absolute) homotopy groups. Then, through the study of various cases, we learn that the classic fibration/cofibration relation does not come automatically. Nonetheless, the ability to see the relative homotopy groups as absolute homotopy groups, in a stronger sense, promises to justify our ultimate search. |
| format | Article |
| id | doaj-art-30d5b0f97e7545ffb4c86f3fd6537bc4 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-30d5b0f97e7545ffb4c86f3fd6537bc42025-08-20T02:38:56ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/2762627626On Relative Homotopy Groups of ModulesC. Joanna Su0Department of Mathematics and Computer Science, Providence College, Providence 02918, RI, USAIn his book “Homotopy Theory and Duality,” Peter Hilton described the concepts of relative homotopy theory in module theory. We study in this paper the possibility of parallel concepts of fibration and cofibration in module theory, analogous to the existing theorems in algebraic topology. First, we discover that one can study relative homotopy groups, of modules, from a viewpoint which is closer to that of (absolute) homotopy groups. Then, through the study of various cases, we learn that the classic fibration/cofibration relation does not come automatically. Nonetheless, the ability to see the relative homotopy groups as absolute homotopy groups, in a stronger sense, promises to justify our ultimate search.http://dx.doi.org/10.1155/2007/27626 |
| spellingShingle | C. Joanna Su On Relative Homotopy Groups of Modules International Journal of Mathematics and Mathematical Sciences |
| title | On Relative Homotopy Groups of Modules |
| title_full | On Relative Homotopy Groups of Modules |
| title_fullStr | On Relative Homotopy Groups of Modules |
| title_full_unstemmed | On Relative Homotopy Groups of Modules |
| title_short | On Relative Homotopy Groups of Modules |
| title_sort | on relative homotopy groups of modules |
| url | http://dx.doi.org/10.1155/2007/27626 |
| work_keys_str_mv | AT cjoannasu onrelativehomotopygroupsofmodules |