Combinatorial integers (m,nj) and Schubert calculus in the integral cohomology ring of infinite smooth flag manifolds

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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Main Authors: Cenap Özel, Erol Yilmaz
Format: Article
Language:English
Published: Hindawi Limited 2006-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/IJMMS/2006/86494
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spelling doaj-d835888449de4690ac29ccacd132e5e82020-11-24T20:58:59ZengHindawi LimitedInternational 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
collection DOAJ
language English
format Article
sources DOAJ
author Cenap Özel
Erol Yilmaz
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
author_facet Cenap Özel
Erol Yilmaz
author_sort Cenap Özel
title 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_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_sort combinatorial integers (m,nj) and schubert calculus in the integral cohomology ring of infinite smooth flag manifolds
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2006-01-01
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].
url http://dx.doi.org/10.1155/IJMMS/2006/86494
work_keys_str_mv AT cenapozel combinatorialintegersmnjandschubertcalculusintheintegralcohomologyringofinfinitesmoothflagmanifolds
AT erolyilmaz combinatorialintegersmnjandschubertcalculusintheintegralcohomologyringofinfinitesmoothflagmanifolds
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