A Class of Open Surfaces with Algorithmically Solvable Homeomorphism Problem

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 two- and three-dimensional manifolds of interest to low-dimensional topologists. Our main result is that the homeomorphism problem in this class is decidable for n=2.