Skip to main content

Polynomial Isoperimetric Inequalities for Richard Thompson’s Groups F, T, and V

  • Conference paper
Algorithmic Problems in Groups and Semigroups

Part of the book series: Trends in Mathematics ((TM))

Abstract

We show that each of the three R. Thompson groups F, T,and V, satisfy polynomial isoperimetric inequality.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.M. Alonso, Inégalités isopérimetriques et quasi-isométries, C. R. Acad. Sci. Paris Sér. 1, 311 (1990), 761–764.

    MathSciNet  MATH  Google Scholar 

  2. G. Baumslag, C.F. Miller, and H. Short, Isoperimetric inequalities and the homology of groups, Invent. Math., 113-3 (1993), 531–560.

    Article  MathSciNet  MATH  Google Scholar 

  3. M.G. Brin, The ubiquity of Thompson’s group F in groups of piecewise linear homeomorphisms of the unit interval, J. London Math. Soc.,to appear.

    Google Scholar 

  4. M.G. Brin and C.C. Squier, Groups of piecewise linear homeomorphisms of the real line, Invent. Math., 79 (1985), 485–498.

    Article  MathSciNet  MATH  Google Scholar 

  5. K.S. Brown, Finiteness properties of groups,J. PureAppl. Algebra, 44 (1987), 45–75.

    Article  MATH  Google Scholar 

  6. K.S. Brown and R. Geoghegan, An infinite-dimentional torsion-free FP group, Invent. Math., 77 (1984), 367–381.

    Article  MathSciNet  MATH  Google Scholar 

  7. J.W. Cannon, W.J. Floyd, and W.R. Parry, Introductorary notes on Richard Thompson’s groups, Enseign. Math. (2), 42 (1996), 215–256.

    MathSciNet  MATH  Google Scholar 

  8. C. Chou, Elementary amenable groups, Illinois J. Math., 24 (1980), 396–407.

    MathSciNet  MATH  Google Scholar 

  9. N. Dershowitz and J.-P. Jouannaud, Rewrite systems, in Handbook of Theoretical Computer Science, J. van Leeuwen, ed., Elsevier Science, Amsterdam, 1990, Chapter 6, 244–320.

    Google Scholar 

  10. S. Gersten, Isoperimetric and isodiametric functions of finite presentations, in Geometric Group Theory, Vol. 1 (Sussex, 1991), London Mathematical Society Lecture Note Series 181, London Mathematical Society, London, 1993, 79–96.

    Chapter  Google Scholar 

  11. S. Gersten, Thompson’s group F is not combable, preprint.

    Google Scholar 

  12. M. Gromov, Hyperbolic groups, in Essays in Group Theory, S. Gersten, ed., MSRI Publications 8, Springer-Verlag, Berlin, New York, Heidelberg, 1987, 75–263.

    Chapter  Google Scholar 

  13. V.S. Guba, Polynomial upper bounds for the Dehn function of R. Thompson’s group F, J. Group Theory, 1 (1998), 203–211.

    Article  MathSciNet  MATH  Google Scholar 

  14. V.S. Guba and M.V. Sapir, Diagram groups, Mem. Amer. Math. Soc., 130-620 (1997), 1–117.

    MathSciNet  Google Scholar 

  15. V.S. Guba and M.V. Sapir, The Dehn function and a regular set of normal forms for R. Thompson’s group F, J. Austral. Math. Soc. Ser. A, 62 (1997), 315–328.

    MathSciNet  MATH  Google Scholar 

  16. V.S. Guba and M.V. Sapir, On subgroups of R. Thompson’s group F and other diagram groups, preprint, 1998.

    Google Scholar 

  17. G. Higman, Finitely Presented Infinite Simple Groups, Notes on Pure Mathematics 8, Australian National University, Canberra, 1974.

    Google Scholar 

  18. V. Kilibarda, On the algebra of semigroup diagrams, Internat. J. Algebra Comput., 7 (1997), 313–338.

    Article  MathSciNet  MATH  Google Scholar 

  19. R. Lyndon and P. Schupp, Combinatorial Group Theory, Springer-Verlag, Berlin, New York, Heidelberg, 1977.

    Google Scholar 

  20. R. McKenzie and R. Thompson, An elementary construction of unsolvable word problems in group theory, in Word Problems, W. W. Boone, F. B. Cannonito, and R. C. Lyndon, eds., Studies in Logic and the Foundations of Mathematics 71, North-Holland, Amsterdam, 1973, 457–478.

    Google Scholar 

  21. K. Madlener and F. Otto, Pseudo-natural algorithms for the word problem for finitely presented monoids and groups, J. Symbolic Comput., 1 (1985), 383–418.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Science+Business Media New York

About this paper

Cite this paper

Guba, V.S. (2000). Polynomial Isoperimetric Inequalities for Richard Thompson’s Groups F, T, and V . In: Birget, JC., Margolis, S., Meakin, J., Sapir, M. (eds) Algorithmic Problems in Groups and Semigroups. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1388-8_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-1388-8_5

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7126-0

  • Online ISBN: 978-1-4612-1388-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics