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.
Constructs tri-Hamiltonian structure and Frobenius manifold for asymmetric gAL hierarchy
Local tri-Hamiltonian structure for Ablowitz-Ladik hierarchy established.
Flows on (or variations of) discrete curves in give rise to flows on a subalgebra of functions on that curve. For a special choice of flows and a certain subalgebra this is described by the Toda lattice hierachy. In the paper it is shown that the canonical symplectic structure on , which can be interpre…
We discuss various aspects of moment map geometry in symplectic and hyperKähler geometry. In particular, we classify complete hyperKähler manifolds of dimension with a tri-Hamiltonian action of a torus of dimension , without any assumption on the finiteness of the Betti numbers. As a result we find that the hyp…
A construction is introduced for modifying hyperkaehler manifolds with tri-Hamiltonian circle action, that in favourable situations increases the second Betti number by one. This is based on the symplectic cut construction of Lerman. In 4 or 8 dimensions the construction may be interpreted as adding a D6-brane. A numbe…
The twist construction is a geometric T-duality that produces new manifolds from old, works well with for example hypercomplex structures and is easily inverted. It tends to destroy properties such as the hyperKähler condition. On the other hand modifications preserve the hyperKähler property, but do not have an obviou…
We classify those manifolds mentioned in the title which have finite topological type. Namely we show any such connected M is isomorphic to a hyperkaehler quotient of a flat quaternionic vector space by an abelian group. We also show that a compact connected and simply connected 3-Sasakian manifold of dimension 4n-1 wh…
In this paper we propose and investigate in full generality new notions of (continuous, non-isometric) symmetry on hyperkähler spaces. These can be grouped into two categories, corresponding to the two basic types of continuous hyperkähler isometries which they deform: tri-Hamiltonian isometries, on one hand, and rotat…