Combinatorial integers (m,nj) and Schubert calculus in the integral cohomology ring of infinite smooth flag manifolds
We discuss the calculation of integral cohomology ring of LG/T and ΩG. First we describe the root system and Weyl group of LG, then we give some homotopy equivalences on the loop groups and homogeneous spaces, and calculate the cohomology ring structures of LG/T and ΩG for affine group A^2. We intro...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/86494 |
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| _version_ | 1850167481223610368 |
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| author | Cenap Özel Erol Yilmaz |
| author_facet | Cenap Özel Erol Yilmaz |
| author_sort | Cenap Özel |
| collection | DOAJ |
| description | We discuss the calculation of integral cohomology ring of LG/T and ΩG. First we describe the root system and Weyl group of LG, then we give some homotopy equivalences on the loop groups and homogeneous spaces, and calculate the cohomology ring structures of LG/T and ΩG for affine group A^2. We introduce combinatorial integers (m,nj) which play a crucial role in our calculations and give some interesting identities among these integers. Last we calculate generators for ideals and rank of each module of graded integral cohomology algebra in the local coefficient ring ℤ[1/2]. |
| format | Article |
| id | doaj-art-d835888449de4690ac29ccacd132e5e8 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d835888449de4690ac29ccacd132e5e82025-08-20T02:21:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/8649486494Combinatorial integers (m,nj) and Schubert calculus in the integral cohomology ring of infinite smooth flag manifoldsCenap Özel0Erol Yilmaz1Department of Mathematics, Abant Izzet Baysal University (AIBU), Golkoy Campus, Bolu 14280, TurkeyDepartment of Mathematics, Abant Izzet Baysal University (AIBU), Golkoy Campus, Bolu 14280, TurkeyWe discuss the calculation of integral cohomology ring of LG/T and ΩG. First we describe the root system and Weyl group of LG, then we give some homotopy equivalences on the loop groups and homogeneous spaces, and calculate the cohomology ring structures of LG/T and ΩG for affine group A^2. We introduce combinatorial integers (m,nj) which play a crucial role in our calculations and give some interesting identities among these integers. Last we calculate generators for ideals and rank of each module of graded integral cohomology algebra in the local coefficient ring ℤ[1/2].http://dx.doi.org/10.1155/IJMMS/2006/86494 |
| spellingShingle | Cenap Özel Erol Yilmaz Combinatorial integers (m,nj) and Schubert calculus in the integral cohomology ring of infinite smooth flag manifolds International Journal of Mathematics and Mathematical Sciences |
| title | Combinatorial integers (m,nj) and Schubert calculus in the integral cohomology ring of infinite smooth flag manifolds |
| title_full | Combinatorial integers (m,nj) and Schubert calculus in the integral cohomology ring of infinite smooth flag manifolds |
| title_fullStr | Combinatorial integers (m,nj) and Schubert calculus in the integral cohomology ring of infinite smooth flag manifolds |
| title_full_unstemmed | Combinatorial integers (m,nj) and Schubert calculus in the integral cohomology ring of infinite smooth flag manifolds |
| title_short | Combinatorial integers (m,nj) and Schubert calculus in the integral cohomology ring of infinite smooth flag manifolds |
| title_sort | combinatorial integers m nj and schubert calculus in the integral cohomology ring of infinite smooth flag manifolds |
| url | http://dx.doi.org/10.1155/IJMMS/2006/86494 |
| work_keys_str_mv | AT cenapozel combinatorialintegersmnjandschubertcalculusintheintegralcohomologyringofinfinitesmoothflagmanifolds AT erolyilmaz combinatorialintegersmnjandschubertcalculusintheintegralcohomologyringofinfinitesmoothflagmanifolds |