Algebraic & Geometric Topology

Coverings and minimal triangulations of $3$–manifolds

William Jaco, J Hyam Rubinstein, and Stephan Tillmann

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Abstract

This paper uses results on the classification of minimal triangulations of 3–manifolds to produce additional results, using covering spaces. Using previous work on minimal triangulations of lens spaces, it is shown that the lens space L(4k,2k1) and the generalised quaternionic space S3Q4k have complexity k, where k2. Moreover, it is shown that their minimal triangulations are unique.

Article information

Source
Algebr. Geom. Topol., Volume 11, Number 3 (2011), 1257-1265.

Dates
Received: 28 February 2009
Revised: 27 June 2009
Accepted: 23 July 2009
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715227

Digital Object Identifier
doi:10.2140/agt.2011.11.1257

Mathematical Reviews number (MathSciNet)
MR2801418

Zentralblatt MATH identifier
1229.57010

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57N10: Topology of general 3-manifolds [See also 57Mxx]

Keywords
$3$–manifold minimal triangulation layered triangulation efficient triangulation complexity prism manifold small Seifert fibred space

Citation

Jaco, William; Rubinstein, J Hyam; Tillmann, Stephan. Coverings and minimal triangulations of $3$–manifolds. Algebr. Geom. Topol. 11 (2011), no. 3, 1257--1265. doi:10.2140/agt.2011.11.1257. https://projecteuclid.org/euclid.agt/1513715227


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References

  • B A Burton, Minimal triangulations and normal surfaces, PhD thesis, University of Melbourne (2003)
  • W Jaco, J H Rubinstein, Layered-triangulations of $3$–manifolds
  • W Jaco, J H Rubinstein, $0$–efficient triangulations of $3$–manifolds, J. Differential Geom. 65 (2003) 61–168
  • W Jaco, J H Rubinstein, S Tillmann, Minimal triangulations for an infinite family of lens spaces, J. Topol. 2 (2009) 157–180
  • S V Matveev, Complexity theory of three-dimensional manifolds, Acta Appl. Math. 19 (1990) 101–130
  • P Orlik, Seifert manifolds, Lecture Notes in Math. 291, Springer, Berlin (1972)
  • J H Rubinstein, On $3$–manifolds that have finite fundamental group and contain Klein bottles, Trans. Amer. Math. Soc. 251 (1979) 129–137