On differential operators over a map, thick morphisms of supermanifolds, and symplectic micromorphisms

TL;DR

This paper explores differential operators over smooth maps, including their formal and quantum versions, and examines their roles in thick morphisms and symplectic micromorphisms within supergeometry.

Contribution

It introduces and analyzes differential operators over maps, including formal and quantum variants, and connects these to thick morphisms and symplectic micromorphisms.

Findings

Construction of differential operators over maps including formal and quantum types

Examples involving pullbacks by thick morphisms

Quantization of symplectic micromorphisms

Abstract

We recall the notion of a differential operator over a smooth map (in linear and non-linear settings) and consider its versions such as formal $\hbar$-differential operators over a map. We study constructions and examples of such operators, which include pullbacks by thick morphisms and quantization of symplectic micromorphisms.