The structural invariants of Goursat distributions

Susan Jane Colley, Gary Kennedy, and Corey Shanbrom

Journal of Singularities
volume 28 (2025), 148-180

Received: 28 August 2023. In revised form: 1 November 2024.

DOI: 10.5427/jsing.2025.28f


Abstract:

This is the first of a pair of papers devoted to the local invariants of Goursat distributions. The study of these distributions naturally leads to a tower of spaces over an arbitrary surface, called the monster tower, and thence to connections with the topic of singularities of curves on surfaces. Here we study those invariants of Goursat distributions akin to those of curves on surfaces, which we call structural invariants. In the subsequent paper we will relate these structural invariants to the small growth invariants.


2020 Mathematical Subject Classification:

58A30, 14H20, 53A55, 58A15


Author(s) information:

Susan Jane Colley, Department of Mathematics, Oberlin College, Oberlin, Ohio 44074, USA
email: scolley@oberlin.edu

Gary Kennedy, Ohio State University at Mansfield, 1760 University Drive, Mansfield, Ohio 44906, USA
email: kennedy@math.ohio-state.edu

Corey Shanbrom, California State University, Sacramento, 6000 J St., Sacramento, CA 95819, USA
email: corey.shanbrom@csus.edu