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.
Local positive definite Z2^n-superfunctions can be extended.
We study the relation between the Laplacian associated to an odd metric on a supermanifold and harmonic superfunctions, through the application of the calculus of variations to a supersymmetric sigma model.
The purpose of this work is to study Lie superalgebroid structures on the space of superdifferential -forms over the supermanifolds whose superfunctions are the differential forms on its underlying manifold. These superalgbroids are constructed from graded Poisson structures defined on the latter superalgebra.
The transformation formula of the Berezin integral holds, in the non-compact case, only up to boundary integrals, which have recently been quantified by Alldridge-Hilgert-Palzer. We establish divergence theorems in semi-Riemannian supergeometry by means of the flow of vector fields and these boundary integrals, and sho…
We discuss of the conceptual difficulties connected with the anticommutativity of classical fermion fields, and we argue that the "space" of all classical configurations of a model with such fields should be described as an infinite-dimensional supermanifold M. We discuss the two main approaches to supermanifolds, and …
In this paper we analyze the notion of morphisms of rings of superfunctions which is the basic concept underlying the definition of supermanifolds as ringed spaces (i.e. following Berezin, Leites, Manin, etc.). We establish a representation formula for all morphisms from the algebra of functions on an ordinary manifold…
Let M_0=G_0/H be a (pseudo)-Riemannian homogeneous spin manifold, with reductive decomposition g_0=h+m and let S(M_0) be the spin bundle defined by the spin representation Ad:H->\GL_R(S) of the stabilizer H. This article studies the superizations of M_0, i.e. its extensions to a homogeneous supermanifold M=G/H whose sh…