Graham Higman's lectures on januarials

TL;DR

This paper summarizes Graham Higman's lectures on januarials, which are coset graphs related to triangle group actions that form 2-face maps on orientable surfaces, providing insights into their structure and properties.

Contribution

It offers a detailed account of januarials, connecting group actions with topological maps, and introduces new perspectives on their combinatorial and geometric features.

Findings

Januarials are coset graphs associated with triangle group actions.

They form 2-face maps when embedded in orientable surfaces.

The paper explores their structural properties and classification.

Abstract

This is an account of a series of lectures of Graham Higman on "januarials", namely coset graphs for actions of triangle groups which become 2-face maps when embedded in orientable surfaces.