The Goldman bracket characterizes homeomorphisms between non-compact surfaces
Geometric Topology
2025-10-15 v2
Abstract
We show that a homotopy equivalence between two non-compact 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.
Cite
@article{arxiv.2307.02769,
title = {The Goldman bracket characterizes homeomorphisms between non-compact surfaces},
author = {Sumanta Das and Siddhartha Gadgil and Ajay Kumar Nair},
journal= {arXiv preprint arXiv:2307.02769},
year = {2025}
}
Comments
to appear in Algebraic and Geometric Topology