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Non-existence of tight neighborly triangulated manifolds with β1 = 2
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N. Singh
Published/Copyright:
July 8, 2014
Abstract
All triangulated d-manifolds satisfy the inequality 
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 S1 with β1 = 1 was constructed by Kühnel in 1986. In this paper, it is shown that there does not exist a tight neighborly triangulated manifold with β1 = 2. In other words, there is no tight neighborly triangulation of (Sd-1x S1)#2 or (Sd-1x̲ S1)#2 for d ≥ 3. A short proof of the uniqueness of Kühnel’s complexes for d ≥ 4 under the assumption β1≠ 0 is also presented.
Published Online: 2014-7-8
Published in Print: 2014-7-1
© 2014 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Masthead
- On axiomatic definitions of non-discrete affine buildings
- On Clifford analysis for holomorphic mappings
- Universal points of convex bodies and bisectors in Minkowski spaces
- The equal tangents property
- Some theorems of harmonic maps for Finsler manifolds
- The regular Grünbaum polyhedron of genus 5
- On the existence of nilsolitons on 2-step nilpotent Lie groups
- Rotational linear Weingarten hypersurfaces in the Euclidean sphere Sn+1
- Spacelike hypersurfaces in anti-de Sitter space
- The group of strong symplectic homeomorphisms in the L∞-metric
- The total Betti number of the intersection of three real quadrics
- On the algebraic models of symmetric smooth manifolds
- Non-existence of tight neighborly triangulated manifolds with β1 = 2
