2010/06/28 by Ben Davison, Davison, Ben
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1006.5475
openalex publication_date 2010/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study orientation data, as introduced by Kontsevich and Soibelman in order\nto define well-behaved integration maps from the motivic Hall algebra of\n3-dimensional Calabi-Yau categories to rings of motives. We start with an\nexample that demonstrates the role of orientation data in this story, before\nworking through the technical details. We give an account of orientation data\nin the case of categories of compactly supported sheaves on noncompact\nCalabi-Yau three-folds. We finally study how this structure behaves under\npullbacks along quasi-equivalences of categories, prove Kontsevich and\nSoibelman's conjecture regarding this behaviour, and also some stronger\ntheorems regarding flops and more general tilts.\n