Monotone expansion

TL;DR

This paper constructs explicit monotone expanders using SL_2(R) actions, supported by a product-growth theorem, advancing understanding of expansion properties in mathematical groups.

Contribution

It provides an explicit construction of monotone expanders based on SL_2(R) actions, with a new product-growth theorem for SL_2(R).

Findings

Explicit family of monotone expanders constructed.

Product-growth theorem for SL_2(R) proved.

Expansion properties linked to Mobius actions.

Abstract

This work, following the outline set in [B2], presents an explicit construction of a family of monotone expanders. The family is essentially defined by the Mobius action of SL_2(R) on the real line. For the proof, we show a product-growth theorem for SL_2(R).