2020/03/31 by Jens Niklas Eberhardt, Grégoire Naisse, Arik Wilbert
Mathematics · #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic structures and combinatorial models #Algorithm #Arc (geometry) #Artificial intelligence #Cohomology #Cohomology ring #Computer science #Construct (python library) #Convolution (computer science) #Equivariant cohomology #Fiber #Geometry #Homotopy and Cohomology in Algebraic Topology #Mathematics #Projection (relational algebra) #Pure mathematics #Ring (chemistry) #math.AG #math.QA
paper · pdf · doi:10.1112/jlms.12413
v3, 42 pages, minor corrections, revised version to appear in J. Lond. Math Soc
arxiv created 2020/10/09 · openalex publication_date 2020/12/11 · arxiv updated 2021/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We give a topological description of the two-row Springer fiber over the real numbers. We show its cohomology ring coincides with the oddification of the cohomology ring of the complex Springer fiber introduced by Lauda–Russell. We also realize Ozsváth–Rasmussen–Szabó's odd TQFT from pullbacks and exceptional pushforwards along inclusion and projection maps between hypertori. Using these results, we construct the odd arc algebra as a convolution algebra over components of the real Springer fiber, giving an odd analog of a construction of Stroppel–Webster.