Topological classification of Mobius transformations

TL;DR

This paper classifies linear fractional transformations on the extended complex plane based on their topological conjugacy, providing a topological perspective on their classification.

Contribution

It introduces a topological classification scheme for Mobius transformations, expanding understanding beyond algebraic or geometric approaches.

Findings

Classification of transformations into topological conjugacy classes

Identification of invariants under topological conjugacy

Framework for analyzing Mobius transformations topologically

Abstract

Linear fractional transformations on the extended complex plane are classified up to topological conjugacy. Recall that two transformations f and g are called topologically conjugate if there exists a homeomorphism h such that hg=fh.