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.
Abstract: Generalizes prequantization map for 2-plectic manifolds.
We consider generalizations of symplectic manifolds called n-plectic manifolds. A manifold is n-plectic if it is equipped with a closed, nondegenerate form of degree n+1. We show that higher structures arise on these manifolds which can be understood as the categorified or homotopy analogues of important structures stu…
Symmetries of bundle gerbes modeled using multiplicative vector fields.
Motivated by the relationship between symplectic fibrations and classical Yang-Mills theories, we study the closeness of a -form (n=2,3) defined on the total space of a fibration as a simple model for an abstract field theory. We introduce 2-plectic fibrations and interpret geometrically the corresponding equations …
A manifold is multisymplectic, or more specifically n-plectic, if it is equipped with a closed nondegenerate differential form of degree n+1. In our previous work with Baez and Hoffnung, we described how the `higher analogs' of the algebraic and geometric structures found in symplectic geometry should naturally arise i…
Survey of bundle gerbes in geometry, field theory, and quantization.
In this paper, we study the algebraic properties of the higher analogues of Courant algebroid structures on the direct sum bundle for an -dimensional manifold. As an application, we revisit Nambu-Poisson structures and multisymplectic structures. We prove that the graph of an -vector fi…