A necessary condition for the tightness of odd-dimensional combinatorial manifolds. (January 2016)

• Record Type: Journal Article
• Authors: Spreer, Jonathan
• Is Part Of: European journal of combinatorics. Volume 51(2016:Jan.)
• Page Start: 475
• Page End: 491
• Publication Date: 2016-01
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2015.07.017
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: We present a necessary condition for ( ℓ − 1 ) -connected combinatorial ( 2 ℓ + 1 ) -manifolds to be tight. As a corollary, we show that there is no tight combinatorial three-manifold with first Betti number at most two other than the boundary of the four-simplex and the nine-vertex triangulation of the three-dimensional Klein bottle.