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aequationes mathematicae

, Volume 31, Issue 1, pp 121–141 | Cite as

A graph-theoretical representation of PL-manifolds — A survey on crystallizations

  • M. Ferri
  • C. Gagliardi
  • L. Grasselli
Survey Paper

Abstract

This is a survey of the techniques and results developed by M. Pezzana and his group, which includes, besides the authors, A. Cavicchioli, P. Bandieri and A Donati.

The original concept is that of “contracted triangulation”, which was introduced with the main goal of finding a “minimal” atlas for topological manifolds ([P1 1968], [P2 1974], [P3 1974], [FG2 1979]). Only later did the possibility of deducing a graph-theoretical tool — the crystallization — for representing P.L. manifolds occur as a major aspect of the theory ([P4 1975], [F1 1976]). This leads to an application of graph theory to P.L. topology, which seems not to have been explored before. Recently, other authors outside Italy have independently become interested in this subject.

For the sake of conciseness, definitions and statements often appear in a form other than that of the quoted references.

AMS (1980) subject classification

Primary O5C15, 57M15 Secondary 57Q05 

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Copyright information

© Birkhäuser Verlag 1986

Authors and Affiliations

  • M. Ferri
    • 1
    • 2
    • 3
  • C. Gagliardi
    • 1
    • 2
    • 3
  • L. Grasselli
    • 1
    • 2
    • 3
  1. 1.Dipartimento di MatematicaUniversità di BolognaBolognaItaly
  2. 2.Dipartimento di MatematicaUniversità di ModenaModenaItaly
  3. 3.Dipartimento di MatematicaUniversità di FerraraFerraraItaly

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