Thompson’s Group F
R. Thompson’s group F is introduced and explored. Its elements are described as equivalence classes of tree diagrams and also as continuous piecewise linear functions from the unit interval to itself, and the two descriptions are linked. We give a finite presentation of F along with a presentation on infinitely many generators, which leads to a normal form.
- 20.Cannon, J.W., Floyd, W.J.: What is … Thompson’s group? Not. AMS V. 58, 3, 1112–1113 (2011)Google Scholar
- 45.Halverson, J.: On the dead end depth of Thompson’s Group F. Furman Univ. Elec. J. Undergraduate Math. 15, 5–19 (2011)Google Scholar
- 46.Hartman, Y., Juschenko, K., Tamuz, O., Ferdowsi, P.V.: Thompson’s group F is not strongly amenable. Ergodic Theory Dynam. Syst. 1–5 (2017). https://doi.org/10.1017/etds.2017.49
- 48.Higman, G.: Finitely Presented Infinite Simple Groups. Notes on Pure Mathematics 8, Department of Pure Mathematics, Department of Mathematics, I.A.S. Australian National University, Canberra (1974). MR0376874 (51 #13049)Google Scholar
- 49.Horak, M., Stein, M., Taback, J.: Computing word length in alternate forms of Thompson’s group F (2008). arXiv:0706.3218v2Google Scholar
- 64.Moore, J: Nonassociative Ramsey theory and the amenability of Thompson’s group F. (2012). arXiv:1209.2063v4 [math.GR]Google Scholar
- 78.Thompson, R.: Handwritten notes (1965). http://www.math.binghamton.edu/matt/thompson/thompson-hd_001.pdf and http://www.math.binghamton.edu/matt/thompson/thompson-hd_008.pdf.
- 81.Wajnryb, B., Witowicz, P.: Richard Thompson group F is not amenable. http://front.math.ucdavis.edu/1408.2188
- 85.Wladis, C.W.: Metric properties of Thompson’s groups F(n) and F(n,m). Ph.D. thesis The Graduate School and University Center, CUNY, (ProQuest, 2007)Google Scholar