On the codimension of the abnormal set in step two Carnot groups

TL;DR

This paper proves that in certain step 2 Carnot groups, the abnormal set's codimension is at least three, extending previous results to groups of dimension up to 7 and generalizing earlier findings for free nilpotent groups.

Contribution

It establishes a lower bound on the codimension of the abnormal set for specific step 2 Carnot groups, including all groups up to dimension 7, generalizing prior work.

Findings

Codimension of abnormal set is at least three in certain step 2 Carnot groups.

Result applies to all step 2 Carnot groups of dimension up to 7.

Generalizes previous results for free nilpotent groups.

Abstract

In this article we prove that the codimension of the abnormal set of the endpoint map for certain classes of Carnot groups of step 2 is at least three. Our result applies to all step 2 Carnot groups of dimension up to 7 and is a generalisation of a previous analogous result for step 2 free nilpotent groups.