We extend the contracted triangulation theorem, established for closed PL manifolds by Pezzana in Atti Sem. Mat. Fis. Univ. Modena 23 (1975), to PL manifolds with connected boundary. The result is derived from a general triangulation theorem for quasi-manifolds. Then we found, as a corollary of our main theorem, a graph-theoretical representation for every PL manifold with connected boundary by means of suitable edge-colored graphs, which we still call a "crystallization".
Crystallizations of PL-manifolds with connected boundary / Cavicchioli, Alberto; Gagliardi, Carlo. - In: BOLLETTINO DELL'UNIONE MATEMATICA ITALIANA. A. - ISSN 0392-4033. - STAMPA. - 17-B:(1980), pp. 902-917.
Crystallizations of PL-manifolds with connected boundary
CAVICCHIOLI, Alberto;GAGLIARDI, Carlo
1980
Abstract
We extend the contracted triangulation theorem, established for closed PL manifolds by Pezzana in Atti Sem. Mat. Fis. Univ. Modena 23 (1975), to PL manifolds with connected boundary. The result is derived from a general triangulation theorem for quasi-manifolds. Then we found, as a corollary of our main theorem, a graph-theoretical representation for every PL manifold with connected boundary by means of suitable edge-colored graphs, which we still call a "crystallization".
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