2-manifold recognition is in logspace

TL;DR

This paper demonstrates that determining whether two 2-manifolds are homeomorphic can be efficiently decided within logarithmic space, leveraging Reingold's logspace algorithm for graph connectivity.

Contribution

It establishes that the homeomorphism problem for 2-manifolds is solvable in logspace, providing a significant complexity classification for this topological problem.

Findings

Homeomorphism problem for 2-manifolds is in logspace

Utilizes Reingold's logspace solution for graph connectivity

Advances understanding of computational complexity in topology

Abstract

We prove that the homeomorphism problem for 2-manifolds can be decided in logspace. The proof relies on Reingold's logspace solution to the undirected $s,t$-connectivity problem in graphs.