2025/05/25 by Savelyev, Yasha
#FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2505.19362
To paraphrase, part I constructs a bundle of A ∞ categories given the input of a Hamiltonian fibration over a smooth manifold. Here we show that this bundle is generally non-trivial by a sample computation. One principal application is differential geometric, and the other is about algebraic K-theory of the integers and the rationals. We find new curvature constraint phenomena for smooth and singular G-connections on principal G-bundles over S 4, where G is \operatorname PU (2) or \operatorname Ham (S 2 ). Even for the classical group \operatorname PU (2) these phenomena are inaccessible to known techniques like the Yang-Mills theory. The above mentioned computation is the geometric component used to show that the categorified algebraic K-theory of the integers and the rationals, defined in ~\citeciteSavelyevAlgKtheory following Toën, admits a ℤ injection in degree 4. This gives a path from Floer theory to number theory.