2025/12/05 by Waleed Qaisar, Qaisar, Waleed
Mathematics · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2512.05966
openalex publication_date 2025/12/05 · openalex created_date 2025/12/09 · openalex updated_date 2026/07/28
We upgrade the classical operation of isomonodromic deformations along a path γ to a functor ℙγ between categories of flat connections with logarithmic singularities along a divisor D, which itself depends functorially on γ, using tools from the theory of Lie groupoids. As applications, (1) we get that isomonodromy gives a map of moduli stacks of flat connections with logarithmic singularities, (2) we encode higher homotopical information at level 2, i.e. we get an action of the fundamental 2-groupoid of the base of our family on the categories of logarithmic flat connections on the fibres, and (3) our methods produce a geometric incarnation of the isomonodromy functors as Morita equivalences which are more primary than the isomonodromy functors themselves, and from which they can be formally extracted by passing to representation categories.