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Rewriting systems for the surface classification theorem

Published online by Cambridge University Press:  27 May 2010

GABRIELE PULCINI
GABRIELE PULCINI*
Affiliation:
Département d'Informatique, École Normale Supérieure, Paris, 45, rue d'Ulm – F-75230 Paris Cedex 05 – France Email: pulcini@di.ens.fr
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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.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 20 , Issue 4 , August 2010 , pp. 577 - 588
Copyright
Copyright © Cambridge University Press 2010

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