Deficiencies of Lattice Subgroups of Lie Groups

TL;DR

This paper investigates the properties of lattices in connected Lie groups, demonstrating that most have nonpositive deficiency except for some special cases, thereby advancing understanding of their algebraic structure.

Contribution

It establishes that, with few exceptions, lattices in connected Lie groups have nonpositive deficiency, clarifying their algebraic and geometric properties.

Findings

Most lattices in connected Lie groups have nonpositive deficiency.

Identifies specific exceptional cases with positive deficiency.

Provides new insights into the structure of Lie group lattices.

Abstract

Let L be a lattice in a connected Lie group. We show that besides a few exceptional cases, the deficiency of L is nonpositive.