163
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

A Construction Principle for Tight and Minimal Triangulations of Manifolds

, , &

References

  • [Alexandrov 38] A. D. Alexandrov. “On A Class of Closed Surfaces.” Recueil Math. (Moscow) 4 (1938), 69–72.
  • [Bagchi 15] B. Bagchi. “A Tightness Criterion for Homology Manifolds with or Without Boundary.” Eur. J. Combin. 46 (2015), 10–15.
  • [Bagchi and Datta 13] B. Bagchi and B. Datta. “On k-Stellated and k-Stacked Spheres.” Discrete Math. 313 (2013), 2318–2329.
  • [Bagchi and Datta 14] B. Bagchi and B. Datta. “On Stellated Spheres and a Tightness Criterion for Combinatorial Manifolds.” Eur. J. Combin. 36 (2014), 294–313.
  • [Bagchi et al. 16] B. Bagchi, B. Datta, and J. Spreer. “Tight Triangulations of Closed 3-Manifolds.” Eur. J. Combin. 54 (2016), 294–313.
  • [Bagchi et al.] B. Bagchi, B. Datta, J. Spreer. “A Characterization of Tightly Triangulated 3-Manifolds.” arXiv:1601.00065 [math.GT].
  • [Bagchi et al.] B. Bagchi, B. A. Burton, B. Datta, N. Singh, and J. Spreer. “Efficient Algorithms to Decide Tightness.” 32nd International Symposium on Computational Geometry (SoCG 2016). In: Leibniz International Proceedings in Informatics (LIPICS) 51 (2016), 12:1–12:15.
  • [Burton et al. 15] B. A. Burton, B. Datta, N. Singh, and J. Spreer. “Separation Index of Graphs and Stacked 2-Spheres.” J. Combin. Theory (A) 136 (2015), 184–197.
  • [Burton et al.] B. A. Burton, B. Datta, N. Singh, and J. Spreer. “Full List of Examples From.” A Construction Principle for Tight and Minimal Triangulations of Manifolds. Available online http://arxiv.org/src/1511.04500v2/anc/.
  • [Chern and Lashof 57] S. S. Chern, R. K. Lashof. “On the Total Curvature Of Immersed Manifolds.” Am. J. Math. 79 (1957), 306–318.
  • [Datta and Murai] B. Datta and S. Murai. “On Stacked Triangulated Manifolds.” arXiv:1407.6767 [math.GT].
  • [Datta and Singh 13] B. Datta and N. Singh. “An Infinite Family of Tight Triangulations of Manifolds.” J. Combin. Theory (A) 120 (2013), 2148–2163.
  • [Effenberger 11] F. Effenberger. “Stacked Polytopes and Tight Triangulations of Manifolds.” J. Combin. Theory (A) 118 (2011), 1843–1862.
  • [Effenberger and Spreer 10] F. Effenberger and J. Spreer. “simpcomp – A GAP Toolbox for Simplicial Complexes.” ACM Commun. Comput. Algebra 44:4 (2010), 186–189.
  • [Effenberger and Spreer 16] F. Effenberger and J. Spreer. “simpcomp – A GAP Toolkit For Simplicial Complexes Version 2.1.6, 2009–2016.” Available online (https://github.com/simpcomp-team/simpcomp).
  • [Jungerman and Ringel 80] M. Jungerman and G. Ringel. “Minimal Triangulations on Orientable Surfaces.” Acta Math. 145 (1980), 121–154.
  • [Kalai 87] G. Kalai. “Rigidity and the Lower Bound Theorem 1.” Invent. Math. 88 (1987), 125–151.
  • [Kühnel 95] W. Kühnel. Tight polyhedral submanifolds and tight triangulations, Lecture Notes in Mathematics, 1612. Berlin: Springer-Verlag, 1995.
  • [Kühnel and Lutz 99] W. Kühnel and F. H. Lutz. “A Census of Tight Triangulations.” Period. Math. Hungar. 39:1-3 (1999), 161–183.
  • [Kuiper 59] N. H. Kuiper. “Immersions with Minimal Total Absolute Curvature.” In: Colloque Géom. Diff. Globale (Bruxelles, 1958), pp. 75–88. Louvain: Centre Belge Rech. Math., 1959.
  • [Milnor 94] J. Milnor. “On the Relationship Between the Betti Numbers of a Hypersurface and an Integral of Its Gaussian Curvature (1950).” In: Collected Papers Vol. 1, Geometry, pp. 15–26. Houston, TX: Publish or Perish Inc., 1994.
  • [Murai 15] S. Murai. “Tight Combinatorial Manifolds and Graded Betti Numbers.” Collect. Math. 66 (2015), 367–386.
  • [Ringel 55] G. Ringel. “Wie man die geschlossenen nichtorientierbaren Flächen in möglichst wenig Dreiecke zerlegen kann.” Math. Ann. 130 (1955), 317–326.
  • [Singh 15] N. Singh. “Strongly Minimal Triangulations of and .” Proc. Indian Acad. Sci. (Math Sci.) 125 (2015), 79–102.
  • [Spreer 16] J. Spreer. “Necessary Conditions for the Tightness of Odd-Dimensional Combinatorial Manifolds.” Eur. J. Combin. 51 (2016), 475–491.
  • [Walkup 70] D. W. Walkup. “The Lower Bound Conjecture for 3- and 4-Manifolds.” Acta Math. 125 (1970), 75–107.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.