Rewriting systems for the surface classification theorem

Authors:
Gabriele Pulcini
Affiliations:
Département d'informatique, École normale supérieure, paris, 45, rue d'ulm – f-75230 paris cedex 05 – france email: pulcini@di.ens.fr
Venue:
Mathematical Structures in Computer Science
Year:
2010

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Abstract

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 : or for dealing with words denoting orientable surfaces and nor for 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.