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An infinite family of tight triangulations of manifolds

Authors:

Nitin SinghAuthors Info & Claims

Journal of Combinatorial Theory Series A, Volume 120, Issue 8

Pages 2148 - 2163

https://doi.org/10.1016/j.jcta.2013.08.005

Published: 01 November 2013 Publication History

Abstract

We give explicit construction of vertex-transitive tight triangulations of d-manifolds for d>=2. More explicitly, for each d>=2, we construct two (d^2+5d+5)-vertex neighborly triangulated d-manifolds whose vertex-links are stacked spheres. The only other non-trivial series of such tight triangulated manifolds currently known is the series of non-simply connected triangulated d-manifolds with 2d+3 vertices constructed by Kuhnel. The manifolds we construct are strongly minimal. For d>=3, they are also tight neighborly as defined by Lutz, Sulanke and Swartz. Like Kuhnel@?s complexes, our manifolds are orientable in even dimensions and non-orientable in odd dimensions.

References

[1]

Bagchi, B. and Datta, B., Minimal triangulations of sphere bundles over the circle. J. Combin. Theory Ser. A. v115. 737-752.

Digital Library

[2]

Bagchi, B. and Datta, B., Lower bound theorem for normal pseudomanifolds. Expo. Math. v26. 327-351.

[3]

On Walkup's class K(d) and a minimal triangulation of (S3¿S1)#3. Discrete Math. v311. 989-995.

[4]

Bagchi, B. and Datta, B., On k-stellated and k-stacked spheres. Discrete Math. v313. 2318-2329.

[5]

Bagchi, B. and Datta, B., On stellated spheres and a tightness criterion for combinatorial manifolds. European J. Combin. v36. 294-313.

Digital Library

[6]

Chestnut, J., Sapir, J. and Swartz, E., Enumerative properties of triangulations of spherical bundles over S1. European J. Combin. v29. 662-671.

Digital Library

[7]

arXiv:1207.6182v2

[8]

tom Dieck, T., Algebraic Topology. 2008. EMS Textbk. Math., 2008.European Math. Soc., Zürich.

[9]

Effenberger, F., Stacked polytopes and tight triangulations of manifolds. J. Combin. Theory Ser. A. v118. 1843-1862.

Digital Library

[10]

http://www.igt.uni-stuttgart.de/LstDiffgeo/simpcomp

[11]

Kalai, G., Rigidity and the lower bound theorem. I. Invent. Math. v88. 125-151.

[12]

Kühnel, W., Higher dimensional analogues of Császár's torus. Results Math. v9. 95-106.

[13]

Kühnel, W., Tight Polyhedral Submanifolds and Tight Triangulations. 1995. Lecture Notes in Math., 1995.Springer-Verlag, Berlin.

[14]

Lutz, F.H., Sulanke, T. and Swartz, E., f-Vector of 3-manifolds. Electron. J. Combin. v16. 1-33.

[15]

Novik, I. and Swartz, E., Socles of Buchsbaum modules, complexes and posets. Adv. Math. v222. 2059-2084.

[16]

Ringel, G., Map Color Theorem. 1974. Springer-Verlag, New York, Heidelberg.

[17]

N. Singh, Non-existence of tight neighborly triangulated manifolds with ß1=2, Adv. Geom., to appear.

[18]

arXiv:1306.5542v1

[19]

Steenrod, N., The Topology of Fibre Bundles. 1951. Princeton Univ. Press, Princeton.

[20]

Walkup, D.W., The lower bound conjecture for 3- and 4-manifolds. Acta Math. v125. 75-107.

Cited By

Spreer J(2016)A necessary condition for the tightness of odd-dimensional combinatorial manifoldsEuropean Journal of Combinatorics10.1016/j.ejc.2015.07.01751:C(475-491)Online publication date: 1-Jan-2016
https://dl.acm.org/doi/10.1016/j.ejc.2015.07.017
Burton BDatta BSingh NSpreer J(2015)Separation index of graphs and stacked 2-spheresJournal of Combinatorial Theory Series A10.1016/j.jcta.2015.07.001136:C(184-197)Online publication date: 1-Nov-2015
https://dl.acm.org/doi/10.1016/j.jcta.2015.07.001

An infinite family of tight triangulations of manifolds
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
2. Theory of computation

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Published In

cover image Journal of Combinatorial Theory Series A

Journal of Combinatorial Theory Series A Volume 120, Issue 8

November, 2013

260 pages

ISSN:0097-3165

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Copyright © Elsevier Inc. © 2013.

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Academic Press, Inc.

United States

Publication History

Published: 01 November 2013

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Cited By

Spreer J(2016)A necessary condition for the tightness of odd-dimensional combinatorial manifoldsEuropean Journal of Combinatorics10.1016/j.ejc.2015.07.01751:C(475-491)Online publication date: 1-Jan-2016
https://dl.acm.org/doi/10.1016/j.ejc.2015.07.017
Burton BDatta BSingh NSpreer J(2015)Separation index of graphs and stacked 2-spheresJournal of Combinatorial Theory Series A10.1016/j.jcta.2015.07.001136:C(184-197)Online publication date: 1-Nov-2015
https://dl.acm.org/doi/10.1016/j.jcta.2015.07.001

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