Solvable groups and a shear construction

TL;DR

This paper introduces a shear construction method that uses one-dimensional foliations to build solvable Lie groups from Abelian groups, expanding geometric models related to T-duality and nilmanifolds.

Contribution

It presents a novel shear construction technique utilizing foliations to generate solvable Lie groups from Abelian groups, broadening geometric modeling tools.

Findings

Shear construction can produce solvable Lie groups from Abelian groups.

The method extends geometric models related to T-duality.

Examples of geometric structures obtained via shear are discussed.

Abstract

The twist construction is a geometric model of T-duality that includes constructions of nilmanifolds from tori. This paper shows how one-dimensional foliations on manifolds may be used in a shear construction, which in algebraic form builds certain solvable Lie groups from Abelian ones. We discuss other examples of geometric structures that may be obtained from the shear construction.