Enumerative properties of triangulations of spherical bundles over S 1

We give a complete characterization of all possible pairs ( f 0 , f 1 ) , where f 0 is the number of vertices and f 1 is the number of edges, of any triangulation of an S k -bundle over S 1 . The main point is that Kühnel’s triangulations of S 2 k + 1 × S 1 and the nonorientable S 2 k -bundle over S...

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Bibliographic Details
Published inEuropean journal of combinatorics Vol. 29; no. 3; pp. 662 - 671
Main Authors Chestnut, Jacob, Sapir, Jenya, Swartz, Ed
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.04.2008
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Summary:We give a complete characterization of all possible pairs ( f 0 , f 1 ) , where f 0 is the number of vertices and f 1 is the number of edges, of any triangulation of an S k -bundle over S 1 . The main point is that Kühnel’s triangulations of S 2 k + 1 × S 1 and the nonorientable S 2 k -bundle over S 1 are unique among all triangulations of ( n − 1 ) -dimensional homology manifolds with 2 n + 1 vertices, first Betti number nonzero, and whose orientation double cover has vanishing second Betti number.
ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2007.03.005