2009/07/25 by Dinesh Deshpande, Deshpande, Dinesh · 2 citations
Mathematics · #14F43 #20G10 #Advanced Topics in Algebra #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #math.AT #msc:14F43 #msc:20G10
paper · pdf · doi:10.48550/arxiv.0907.4437
20 pages
arxiv created 2009/07/25 · openalex publication_date 2009/07/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define algebraic cobordism of classifying spaces, Ω^*(BG) and G-equivariant algebraic cobordism Ω^*G(-) for a linear algebraic group G. We prove some properties of the coniveau filtration on algebraic cobordism, denoted Fj(Ω^*(-)), which are required for the definition to work. We show that G-equivariant cobordism satisfies the localization exact sequence. We calculate Ω^*(BG) for algebraic groups over the complex numbers corresponding to classical Lie groups GL(n), SL(n), Sp(n), O(n) and SO(2n+1). We also calculate Ω^*(BG) when G is a finite abelian group. A finite non-abelian group for which we calculate Ω^*(BG) is the quaternion group of order 8. In all the above cases, we check that Ω^*(BG) is isomorphic to MU^*(BG).