Rewriting systems for the surface classification theorem
Gabriele Pulcini · Mathematical Structures in Computer Science · 2010
The work reported in this paper refers to Massey's proof of the surface classification theorem based on the standard word-rewriting treatment of surfaces. We arrange this approach into a formal rewriting system and provide a new version of Massey's argument. Moreover, we study the computational properties of two subsystems of : orfor dealing with words denoting orientable surfaces and norfor dealing with words denoting non-orientable surfaces. We show how such properties induce an alternative proof for the surface classification in which the basic homeomorphism between the connected sum of three projective planes and the connected sum of a torus with a projective plane is not required.