2011/05/20 by Stefan Müller–Stach, Chris Peters, Müller-Stach, Stefan +3
Mathematics · #14C30 #14K10 #19K56 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1105.4108
openalex publication_date 2011/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We look into a construction of principal abelian varieties attached to\ncertain spin manifolds, due to Witten and Moore-Witten around 2000 and try to\nplace it in a broader framework. This is related to Weil intermediate Jacobians\nbut it also suggests to associate abelian varieties to polarized even weight\nHodge structures. The latter construction can also be explained in terms of\nalgebraic groups which might be useful from the point of view of Tannakian\ncategories. The constructions depend on moduli much as in Teichm "uller theory\nalthough the period maps in general are only real analytic. One of the nice\nfeatures is how the index for certain differential operators canonically\nassociated to the geometry of the situation (spin structure, complex structure\netc.) leads to integrality of skew pairings on the topological K-group (coming\nfrom the Index Theorem) which then serves as a polarization for the jacobian.\n