A proof of Kühnel's conjecture for \(n\geq k^ 2+3k\)
type: Item
instance of: scholarly article
title: A proof of Kühnel's conjecture for \(n\geq k^ 2+3k\)
zbMATH Open document ID: 0887.52007
DOI: 10.1007/BF03322172
author: Eric Sparla
published in: Results in Mathematics
publication date: 1998-05-06T00:00:00Z
review text: The Kühnel's conjecture for combinatorial 2k-manifolds has been established by W. Kühnel and U. Brehm if the number \(n\) of vertices of M satisfies either \(n \leq 3k + 3\) or \(n \geq k^2 + 4k + 3\). In this paper, the author improves this result by showing that the conjecture is true for \(n \geq k^2 + 3 k\) and so he obtains as a corollary that the statement in the conjecture is true for \(k = 1\) and \(k = 2\).
Mathematics Subject Classification ID: 52B05
Mathematics Subject Classification ID: 57Q15
zbMATH DE Number: 1029211
zbMATH Keywords: Kühnel's conjecture
zbMATH Keywords: combinatorial manifold
Wikidata QID: Q123002796
reviewed by: Maria do Rosário Pinto
MaRDI profile type: Publication
cites work: Q3972127
cites work: Combinatorial manifolds with few vertices
cites work: Manifolds which are like projective planes
cites work: Q5547252
cites work: Rigidity and the lower bound theorem. I
cites work: On the Number of Vertices of a Convex Polytope
cites work: Q4309963
cites work: Tight polyhedral submanifolds and tight triangulations
cites work: Q5621733
cites work: Q5589310
cites work: The Upper Bound Conjecture and Cohen-Macaulay Rings
description: scientific article; zbMATH DE number 1029211