A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study shows convergence of certain metrics to flat torus.
Metrics of exceptional holonomy are vacuum solutions to the Einstein equation. In this paper we describe manifolds with holonomy contained in Spin(7) preserved by a three-torus symmetry in terms of tri-symplectic geometry of four-manifolds. These complement examples that have appeared in the context of domain wall prob…
This paper establishes that the Nahm transform sending spatially periodic instantons (instantons on the product of the real line and a three-torus) to singular monopoles on the dual three-torus is indeed a bijection as suggested by the heuristic. In the process, we show how the Nahm transform intertwines to a Fourier-M…
Using a recently developed piecewise flat method, numerical evolutions of the Ricci flow are computed for a number of manifolds, using a number of different mesh types, and shown to converge to the expected smooth behaviour as the mesh resolution is increased. The manifolds were chosen to have varying degrees of homoge…
Study nearly parallel G2-structures with torus symmetry using multi-moment maps.
We compute the Ricci curvature of a curved noncommutative three torus. The computation is done both for conformal and non-conformal perturbations of the flat metric. To perturb the flat metric, the standard volume form on the noncommutative three torus is perturbed and the corresponding perturbed Laplacian is analyzed.…
The mapping class group of a Heegaard splitting is the group of connected components in the set of automorphisms of the ambient manifold that map the Heegaard surface onto itself. For the genus three Heegaard splitting of the 3-torus, we find an eight element generating set for this group. Six of these generators induc…
This paper constructs an algebra on a 3-torus with specific properties for fluid dynamics.
The paper studies cohomological Donaldson-Thomas theory for local systems on a 3-torus.
The asymptotic behavior of open plane sections of triply periodic surfaces is dictated, for an open dense set of plane directions, by an integer second homology class of the three-torus. The dependence of this homology class on the direction can have a rather rich structure, leading in special cases to a fractal. In th…
This paper studies isotopies of periodic tangles in 3-manifolds using finite covers.
The paper studies dimensions of attractors for modified Leray-alpha equation on various surfaces.
We prove integral rigidity for Seiberg-Witten invariants of 4-manifolds with specific hypersurfaces.
The study classifies compact Cauchy horizons in vacuum spacetimes.
The paper studies Dirac operators on large spectral three-manifolds.