Residues in group completions and the Cech cohomology of BG

2016/05/17 by Edward Dewey, Dewey, Edward
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #math.AG #math.GT #msc:14L30 #msc:14M17 #msc:55R40

paper · pdf · doi:10.48550/arxiv.1605.05385

14 pages. Section 2 of the previous version was wrong and has been replaced. Also fixed a ubiquitous sign error

arxiv created 2017/03/05 · arxiv updated 2017/03/07

Abstract

Let G be a connected affine algebraic group over ℂ, G → X be an open immersion of G-varieties, Z = X-G and i: Z → X be the inclusion. Let α∈ H^*(G,ℂ) be primitive. We give a method to compute the image of α in H^*(Z, i^!ℂ_X), using a lift of α along the first edge map of the Čech spectral sequence for H^*(BG, ℂ). We apply it to the wonderful compactification of a centerless semisimple group G.

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