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An equivalence criterion for PL-manifolds

Casali, Maria Rita (2002) An equivalence criterion for PL-manifolds. Rendiconti del Seminario della Facoltà di Scienze dell'Università di Cagliari, 72 (2). pp. 2-17. ISSN 0370727X

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Abstract

Aim of the paper is to translate the homeomorphism problem for n-dimensional PL-manifolds, with or without boundary, into an equivalence problem for pseudosimplicial triangulations (i.e. a suitable generalization of simplicial triangulations, where two (curvilinear) simplices may intersect in more than one face), by means of a finite number of moves, called (geometric) dipole moves. Note that the environment of the present work is closely related to the representation method for PL-manifolds via edge-colorured graphs, since (n+1)-coloured graphs representing n-manifolds are a «discrete way» to visualize suitable pseudosimplicial triangulations. From the graphtheoretical point of view, the equivalence problem was already faced – and solved – in [FG] for closed n-manifolds and in [C2] in the general 3-dimensional setting; here, the equivalence criterion via (geometric) dipole moves is proved to hold for the whole class of PL n-manifolds; moreover, it is proved to be equivariant with respect to boundary triangulation.

Item Type:Article
Date:2002
Institution:Università degli Studi di Cagliari
Divisions:Centri > Seminario Scientifico della Facolta' di Scienze MM.FF.NN.
Subjects:Area 01 - Scienze matematiche e informatiche > MAT/03 Geometria
Uncontrolled Keywords:Homeomorphism problem, PL-manifolds, pseudosimplicial triangulations, 57Q15 - 57N15 - 57M15
ID Code:267
Deposited On:11 Nov 2008 09:23

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