2023/02/08 by Albin Grataloup, Grataloup, Albin
Mathematics · Physics and Astronomy · #14A30 #14D15 #14F43 #18G10 #18N60 #18N70 #53D12 #53D17 #53D20 #70S99 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2302.04036
openalex publication_date 2023/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by the cohomological construction for the BV formalism from physics, this thesis asks how to perform the intersections and quotients appearing in the BV construction. This leads to the study of the derived symplectic reduction and the extension of these classical notions for group action and infinitesimal actions of Lie algebroids. In this context, we generalize the classical notion of moment maps for global and infinitesimal actions. We then study examples of such moment maps and their derived reductions and produce new shifted examples through a procedure of derived Lagrangian intersection. We then motivate why these new examples can bring a new geometric understanding of the BV complex as a generalized shifted symplectic reduction.