Francis Bischoff

activity

20232026

collaborators

4 papers

math.DG2026

Polynomial degeneration and the Poisson geometry of truncated polynomials

Francis Bischoff, Aldo Witte

We develop a formalism for studying geometric structures that degenerate to polynomial order along a hypersurface $W \subset M$ . We then demonstrate it in the study of Poisson geom…

math.DG2025

$b^{k}$ -algebroids and the variety of foliation jets

Francis Bischoff, Álvaro del Pino, Aldo Witte

We introduce and classify singular foliations of $b^{k + 1}$ -type, which formalize the properties of vector fields that are tangent to a submanifold $W \subset M$ to order $k$ . When…

math.AT2025

Thin homotopy and the signature of piecewise linear surfaces

Francis Bischoff, Darrick Lee

We introduce a crossed module of piecewise linear surfaces and study the signature homomorphism, defined as the surface holonomy of a universal translation invariant $2$ -connection…

math.DG2023

Jets of foliations and $b^{k}$ -algebroids

Francis Bischoff, Álvaro del Pino, Aldo Witte

In this article, we introduce and study singular foliations of $b^{k}$ -type. These singular foliations formalize the properties of vector fields that are tangent to order $k$ along a…

Polynomial degeneration and the Poisson geometry of truncated polynomials

bk-algebroids and the variety of foliation jets

Thin homotopy and the signature of piecewise linear surfaces

Jets of foliations and bk-algebroids

$b^{k}$ -algebroids and the variety of foliation jets

Jets of foliations and $b^{k}$ -algebroids