Publicacions Matemàtiques

Polygonal $\mathcal{VH}$ Complexes

Jason K. C. Polák and Daniel T. Wise

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Abstract

Ian Leary inquires whether a class of hyperbolic finitely presented groups are residually finite. We answer in the affirmative by giving a systematic version of a construction in his paper, which shows that the standard $2$-complexes of these presentations have a $\mathcal{VH}$-structure. This structure induces a splitting of these groups, which together with hyperbolicity, implies that these groups are residually finite.

Article information

Source
Publ. Mat., Volume 57, Number 2 (2013), 421-428.

Dates
First available in Project Euclid: 12 December 2013

Permanent link to this document
https://projecteuclid.org/euclid.pm/1386857702

Mathematical Reviews number (MathSciNet)
MR3114776

Zentralblatt MATH identifier
1286.20056

Subjects
Primary: 20F67: Hyperbolic groups and nonpositively curved groups

Keywords
Residually finite group hyperbolic group nonpositively curved cube complex

Citation

Polák, Jason K. C.; Wise, Daniel T. Polygonal $\mathcal{VH}$ Complexes. Publ. Mat. 57 (2013), no. 2, 421--428. https://projecteuclid.org/euclid.pm/1386857702


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References

  • M. R. Bridson, On the existence of flat planes in spaces of nonpositive curvature, Proc. Amer. Math. Soc. 123(1) (1995), 223\Ndash235. \small\tt DOI: 10.2307/2160630.
  • S. M. Gersten and H. Short, Small cancellation theory and automatic groups: Part II, Invent. Math. 105(3) (1991), 641\Ndash662. \small\tt DOI: 10.1007/BF01232283.
  • I. J. Leary, A metric Kan-Thurston theorem, Preprint. \small\tt arXiv: \small\tt 1009.1540.
  • D. T. Wise, The structure of groups with a quasiconvex hierar-chy, submitted. Available at:\!\! \small\tt http://www.math.mcgill.ca/wise/ \small\tt papers.
  • D. T. Wise, Subgroup separability of the figure 8 knot group,Topology 45(3) (2006), 421\Ndash463. \small\tt DOI: 10.1016/j.top.2005.06. \small\tt 004.