An alternate proof of Wise's Malnormal Special Quotient Theorem

TL;DR

This paper presents an alternative proof of Wise's Malnormal Special Quotient Theorem that bypasses cubical small cancellation theory and connects it to Wise's Quasiconvex Hierarchy Theorem.

Contribution

It provides a new proof of MSQT without cubical small cancellation, and links it to Wise's Quasiconvex Hierarchy Theorem using existing theorems.

Findings

Alternative proof of MSQT avoiding cubical small cancellation

Derivation of Wise's Quasiconvex Hierarchy Theorem from MSQT

Connections established between key theorems in geometric group theory

Abstract

We give an alternate proof of Wise's Malnormal Special Quotient Theorem (MSQT), avoiding cubical small cancellation theory. We also show how to deduce Wise's Quasiconvex Hierarchy Theorem from the MSQT and theorems of Hsu--Wise and Haglund--Wise.