A class of open surfaces with algorithmically solvable homeomorphism problem
arXiv:1209.2818
Abstract
We introduce a new class of possibly noncompact n-dimensional manifolds without boundary associated to finite data which we call topological automata. This class is large enough to contain many interesting examples of open 2-dimensional and 3-dimensional manifolds of interest to low-dimensional topologists. Our main result is that the homeomorphism problem in this class is decidable for n = 2.
Title, abstract have changed. Introduction and concluding remarks substantially rewritten
References in corpus (7)
- Ricci flow with surgery on three-manifolds
- Big mapping class groups: an overview
- Large scale geometry of big mapping class groups
- Automatic continuity for homeomorphism groups of noncompact manifolds
- Wild translation surfaces and infinite genus
- Computable structures on topological manifolds
- One-ended 3-manifolds without locally finite toric decompositions