2025/07/13 by Frédéric Rochon, Rochon, Frédéric
Mathematics · Physics and Astronomy · #53C26 #53D20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2507.09451
openalex publication_date 2025/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that simply connected toric hyperKähler metrics of finite topological type with maximal volume growth are generically quasi-asymptotically conical, which allows us to compute explicitly their reduced L2-cohomology groups. In the asymptotically conical case, we also provide a fine description of the geometry at infinity of their Taub-NUT deformations of order 1 in terms of a compactification by a manifold with corners, which allows us to show that those deformations are of bounded geometry, to estimate their curvature at infinity and their volume growth and to identify uniquely their tangent cone at infinity. In many instances, the dimension of this tangent cone at infinity is strictly smaller than the order of the volume growth. Finally, our methods show that the Taub-NUT deformations of maximal order of the Euclidean metric are quasi-fibered boundary metrics, which allows us to identify uniquely their tangent cone at infinity, to compute their reduced L2 cohomology groups and to prove that Sen's S-duality conjecture holds for centered monopoles of type (1,1,…,1).