The complex cobordism of \(BSO_n\)
type: Item
instance of: scholarly article
title: The complex cobordism of \(BSO_n\)
zbMATH Open document ID: 1200.55008
DOI: 10.1215/0023608X-2009-015
author: Koichi Inoue
author: Nobuaki Yagita
published in: Kyoto Journal of Mathematics
publication date: 2010-07-13T00:00:00Z
review text: This paper computes \(MU^{*}(BSO(2m))\). The authors show that it is generated as an \(MU^{*}\)-algebra by Conner-Floyd Chern classes \(c_{i}\) and one \(2m\)-dimensional element \(y_{m}\). Using a result of Totaro that for algebraic groups \(G\) the classifying spaces are approximated by algebraic varieties one can compute the Chow ring of \(BG\). The arguments use the stratification method introduced by Verosi, but without the algebraic geometry results. Results are also obtained for the Morava \(K\)-theory of \(BSO _{2m+1}\)
Mathematics Subject Classification ID: 55N22
Mathematics Subject Classification ID: 57R75
Mathematics Subject Classification ID: 55N91
Mathematics Subject Classification ID: 57R85
Mathematics Subject Classification ID: 14C15
zbMATH DE Number: 5735952
zbMATH Keywords: Chow Ring
zbMATH Keywords: Chern Class, Brown-Peterson theory
zbMATH Keywords: \(MU\)
zbMATH Keywords: stratification
reviewed by: Jonathan Hodgson
MaRDI profile type: Publication
cites work: Equivariant intersection theory (With an appendix by Angelo Vistoli: The Chow ring of \({\mathcal M}_2\))
cites work: The Chow rings of G 2 and Spin(7)
cites work: The Brown-Peterson cohomology of \(BSO(6)\)
cites work: Brown-Peterson and Ordinary Cohomology Theories of Classifying Spaces for Compact Lie Groups
cites work: Morava \(K\)-theory of classifying spaces: Some calculations
cites work: Algebraic cobordism. I
cites work: Algebraic cobordism. II
cites work: On the Chow rings of classifying spaces for classical groups
cites work: \(\mathbb{A}^1\)-homotopy theory of schemes
cites work: Equivariant Chow rings of O(k), SO(2k+1), and SO(4)
cites work: Brown-Peterson cohomology from Morava \(K\)-theory
cites work: Q4061677
cites work: Q4946334
cites work: On the Chow ring of the classifying stack of PGL3,ℂ
cites work: On the cohomology and the Chow ring of the classifying space of PGL p
cites work: The Complex Cobordism of BO n
description: scientific article; zbMATH DE number 5735952