The Goldman bracket characterizes homeomorphisms between noncompact surfaces

Das, Sumanta; Gadgil, Siddhartha; Nair, Ajay Kumar

doi:10.2140/agt.2025.25.3585

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

The Goldman bracket characterizes homeomorphisms between noncompact surfaces

Sumanta Das, Siddhartha Gadgil and Ajay Kumar Nair

Algebraic & Geometric Topology 25 (2025) 3585–3601

DOI: 10.2140/agt.2025.25.3585

Abstract

We show that a homotopy equivalence between two noncompact orientable surfaces is homotopic to a homeomorphism if and only if it preserves the Goldman bracket, provided our surfaces are neither the plane nor the punctured plane.

Keywords

Goldman bracket, noncompact surfaces, topological rigidity

Mathematical Subject Classification

Primary: 57K20

References

Publication

Received: 27 July 2023

Revised: 20 March 2024

Accepted: 15 April 2024

Published: 1 October 2025

Authors

Sumanta Das
Department of Mathematics Indian Institute of Science Bangalore India

Siddhartha Gadgil
Department of Mathematics Indian Institute of Science Bangalore India

Ajay Kumar Nair
Department of Mathematics Indian Institute of Science Bangalore India

Open Access made possible by participating institutions via Subscribe to Open.

Volume 25, issue 6 (2025)