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Non-existence of tight neighborly triangulated manifolds with beta(1)=2

Singh, Nitin (2014) Non-existence of tight neighborly triangulated manifolds with beta(1)=2. In: ADVANCES IN GEOMETRY, 14 (3). pp. 561-569.

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Official URL: http://dx.doi.org/ 10.1515/advgeom-2014-0005

Abstract

All triangulated d-manifolds satisfy the inequality ((f0-d-1)(2)) >= ((d+2)(2))beta(1) for d >= 3. A triangulated d-manifold is called tight neighborly if it attains equality in this bound. For each d >= 3, a (2d + 3)-vertex tight neighborly triangulation of the Sd-1-bundle over S-1 with beta(1) = 1 was constructed by Kuhnel in 1986. In this paper, it is shown that there does not exist a tight neighborly triangulated manifold with beta(1) = 2. In other words, there is no tight neighborly triangulation of (Sd-1 x S-1)(#2) or (Sd-1 (sic) S-1)(#2) for d >= 3. A short proof of the uniqueness of K hnel's complexes for d >= 4 under the assumption beta(1) not equal 0 is also presented.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the WALTER DE GRUYTER GMBH, GENTHINER STRASSE 13, D-10785 BERLIN, GERMANY
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 26 Aug 2014 06:33
Last Modified: 26 Aug 2014 06:33
URI: http://eprints.iisc.ac.in/id/eprint/49669

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