2022/03/25 by Marc Levine, Levine, Marc · 1 citation
Mathematics · #14F42 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2203.13882
openalex publication_date 2022/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let N be a normalizer of the diagonal torus T1≅ \mathbbGm in SL2. We prove localization theorems for SL2n and Nn for equivariant cohomology with coefficients in the (twisted) Witt sheaf, along the lines of the classical Atiyah-Bott localization theorems for equivariant cohomology for a torus action. We also have an analog of the Bott residue formula for SL2n and N. In the case of an SL2n-action, there is a rather serious restriction on the orbit type. For an N-action, there is no restriction for the localization result, but for the Bott residue theorem, one requires a certain type of decomposition of the fixed points for the T1-action.