Abstract
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.
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References
Brin, M.G., Squier, C.C.: Groups of piecewise linear homeomorphisms of the real line. Invent. Math. 79, 485–498 (1985)
Brown, K.S.: Finiteness properties of groups. J. Pure Appl. Algebra 44, 45–75 (1987). MR0885095 (88m:20110), Zbl 0613.20033
Cannon, J.W., Floyd, W.J.: What is … Thompson’s group? Not. AMS V. 58, 3, 1112–1113 (2011)
Cannon, J.W., Floyd, W.J., Parry, W.R.: Introductory notes on Richard Thompson’s groups, L’Enseignement Mathematique. Revue Internationale. IIe Serie 42 3, 215–256 (1996)
Cleary, S., Taback, J.: Combinatorial properties of Thompson’s group F. Trans. Am. Math. Soc. 356(7), 2825–2849 (2004)
Fordham, S.B.: Minimal length elements of Thompson’s group F. Geom. Dedicata 99, 179–220 (2003)
Halverson, J.: On the dead end depth of Thompson’s Group F. Furman Univ. Elec. J. Undergraduate Math. 15, 5–19 (2011)
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
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)
Horak, M., Stein, M., Taback, J.: Computing word length in alternate forms of Thompson’s group F (2008). arXiv:0706.3218v2
Moore, J: Nonassociative Ramsey theory and the amenability of Thompson’s group F. (2012). arXiv:1209.2063v4 [math.GR]
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.
Wajnryb, B., Witowicz, P.: Richard Thompson group F is not amenable. http://front.math.ucdavis.edu/1408.2188
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)
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Bonanome, M.C., Dean, M.H., Putnam Dean, J. (2018). Thompson’s Group F . In: A Sampling of Remarkable Groups. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-01978-5_2
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DOI: https://doi.org/10.1007/978-3-030-01978-5_2
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