Rational Cohomology Algebra of Mapping Spaces between Complex Grassmannians
We consider the complex Grassmannian Grk,n of k-dimensional subspaces of ℂn. There is a natural inclusion in,r:Grk,n↪Grk,n+r. Here, we use Sullivan models to compute the rational cohomology algebra of the component of the inclusion in,r in the space of mappings from Grk,n to Grk,n+r for r≥1 and in p...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2020/9385153 |
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| author | Paul Antony Otieno Jean Baptiste Gatsinzi Vitalis Onyango-Otieno |
| author_facet | Paul Antony Otieno Jean Baptiste Gatsinzi Vitalis Onyango-Otieno |
| author_sort | Paul Antony Otieno |
| collection | DOAJ |
| description | We consider the complex Grassmannian Grk,n of k-dimensional subspaces of ℂn. There is a natural inclusion in,r:Grk,n↪Grk,n+r. Here, we use Sullivan models to compute the rational cohomology algebra of the component of the inclusion in,r in the space of mappings from Grk,n to Grk,n+r for r≥1 and in particular to show that the cohomology of mapGrn,k,Grn,k+r;in,r contains a truncated algebra ℚx/xr+n+k2−nk, where x=2, for k≥2 and n≥4. |
| format | Article |
| id | doaj-art-5a2e27414f61412197f8d1be5d330a81 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-5a2e27414f61412197f8d1be5d330a812025-08-20T02:05:29ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252020-01-01202010.1155/2020/93851539385153Rational Cohomology Algebra of Mapping Spaces between Complex GrassmanniansPaul Antony Otieno0Jean Baptiste Gatsinzi1Vitalis Onyango-Otieno2Strathmore Institute of Mathematical Sciences, Strathmore University, 59857 Nairobi, KenyaDepartment of Mathematics, Botswana International University of Science and Technology, Private Bag 16, Palapye, BotswanaStrathmore Institute of Mathematical Sciences, Strathmore University, 59857 Nairobi, KenyaWe consider the complex Grassmannian Grk,n of k-dimensional subspaces of ℂn. There is a natural inclusion in,r:Grk,n↪Grk,n+r. Here, we use Sullivan models to compute the rational cohomology algebra of the component of the inclusion in,r in the space of mappings from Grk,n to Grk,n+r for r≥1 and in particular to show that the cohomology of mapGrn,k,Grn,k+r;in,r contains a truncated algebra ℚx/xr+n+k2−nk, where x=2, for k≥2 and n≥4.http://dx.doi.org/10.1155/2020/9385153 |
| spellingShingle | Paul Antony Otieno Jean Baptiste Gatsinzi Vitalis Onyango-Otieno Rational Cohomology Algebra of Mapping Spaces between Complex Grassmannians International Journal of Mathematics and Mathematical Sciences |
| title | Rational Cohomology Algebra of Mapping Spaces between Complex Grassmannians |
| title_full | Rational Cohomology Algebra of Mapping Spaces between Complex Grassmannians |
| title_fullStr | Rational Cohomology Algebra of Mapping Spaces between Complex Grassmannians |
| title_full_unstemmed | Rational Cohomology Algebra of Mapping Spaces between Complex Grassmannians |
| title_short | Rational Cohomology Algebra of Mapping Spaces between Complex Grassmannians |
| title_sort | rational cohomology algebra of mapping spaces between complex grassmannians |
| url | http://dx.doi.org/10.1155/2020/9385153 |
| work_keys_str_mv | AT paulantonyotieno rationalcohomologyalgebraofmappingspacesbetweencomplexgrassmannians AT jeanbaptistegatsinzi rationalcohomologyalgebraofmappingspacesbetweencomplexgrassmannians AT vitalisonyangootieno rationalcohomologyalgebraofmappingspacesbetweencomplexgrassmannians |