Shift dynamics of the groups of Fibonacci type

References

[1] M. Aschenbrenner, S. Friedl and H. Wilton, 3-Manifold Groups, EMS Ser. Lect. Math, European Mathematical Society, Zürich, 2015. 10.4171/154Search in Google Scholar

[2] V. G. Bardakov and A. Y. Vesnin, On a generalization of Fibonacci groups, Algebra Logika 42 (2003), no. 2, 131–160, 255. 10.1023/A:1025913505208Search in Google Scholar

[3] W. A. Bogley, On shift dynamics for cyclically presented groups, J. Algebra 418 (2014), 154–173. 10.1016/j.jalgebra.2014.07.009Search in Google Scholar

[4] W. A. Bogley and F. W. Parker, Cyclically presented groups with length four positive relators, J. Group Theory 21 (2018), no. 5, 911–947. 10.1515/jgth-2018-0023Search in Google Scholar

[5] W. A. Bogley and S. J. Pride, Aspherical relative presentations, Proc. Edinburgh Math. Soc. (2) 35 (1992), no. 1, 1–39. 10.1017/S0013091500005290Search in Google Scholar

[6] W. A. Bogley and G. Williams, Coherence, subgroup separability, and metacyclic structures for a class of cyclically presented groups, J. Algebra 480 (2017), 266–297. 10.1016/j.jalgebra.2017.02.002Search in Google Scholar

[7] K. S. Brown, Cohomology of Groups, Grad. Texts in Math. 87, Springer, New York, 1982. 10.1007/978-1-4684-9327-6Search in Google Scholar

[8] A. Cavicchioli, F. Hegenbarth and A. C. Kim, A geometric study of Sieradski groups, Algebra Colloq. 5 (1998), no. 2, 203–217. Search in Google Scholar

[9] A. Cavicchioli, E. A. O’Brien and F. Spaggiari, On some questions about a family of cyclically presented groups, J. Algebra 320 (2008), no. 11, 4063–4072. 10.1016/j.jalgebra.2008.07.015Search in Google Scholar

[10] A. Cavicchioli, D. Repovš and F. Spaggiari, Families of group presentations related to topology, J. Algebra 286 (2005), no. 1, 41–56. 10.1016/j.jalgebra.2005.01.008Search in Google Scholar

[11] C. P. Chalk, Fibonacci groups F ⁢ ( 2 , n ) are hyperbolic for 𝑛 odd and n ≥ 11 , J. Group Theory 24 (2021), no. 2, 359–384. 10.1515/jgth-2020-0068Search in Google Scholar

[12] G. Chelnokov and A. Mednykh, On the coverings of Hantzsche–Wendt manifold, preprint (2020), https://arxiv.org/abs/2009.06691. 10.2748/tmj.20210308Search in Google Scholar

[13] I. Chinyere and G. Williams, Hyperbolic groups of Fibonacci type and T(5) cyclically presented groups, J. Algebra 580 (2021), 104–126. 10.1016/j.jalgebra.2021.04.003Search in Google Scholar

[14] J. H. Conway, J. A. Wenzel, R. C. Lyndon and H. Flanders, Problems and solutions: Solutions of advanced problems: 5327, Amer. Math. Monthly 74 (1967), no. 1, 91–93. 10.2307/2314083Search in Google Scholar

[15] M. Edjvet, On the asphericity of one-relator relative presentations, Proc. Roy. Soc. Edinburgh Sect. A 124 (1994), no. 4,713–728. 10.1017/S0308210500028614Search in Google Scholar

[16] N. D. Gilbert and J. Howie, LOG groups and cyclically presented groups, J. Algebra 174 (1995), no. 1, 118–131. 10.1006/jabr.1995.1119Search in Google Scholar

[17] H. Helling, A. C. Kim and J. L. Mennicke, A geometric study of Fibonacci groups, J. Lie Theory 8 (1998), no. 1, 1–23. Search in Google Scholar

[18] J. Howie and G. Williams, Tadpole labelled oriented graph groups and cyclically presented groups, J. Algebra 371 (2012), 521–535. 10.1016/j.jalgebra.2012.09.001Search in Google Scholar

[19] J. Howie and G. Williams, Fibonacci type presentations and 3-manifolds, Topology Appl. 215 (2017), 24–34. 10.1016/j.topol.2016.10.012Search in Google Scholar

[20] D. L. Johnson, Extensions of Fibonacci groups, Bull. Lond. Math. Soc. 7 (1975), 101–104. 10.1112/blms/7.1.101Search in Google Scholar

[21] D. L. Johnson, Topics in the Theory of Group Presentations, London Math. Soc. Lecture Note Ser. 42, Cambridge University, Cambridge, 1980. 10.1017/CBO9780511629303Search in Google Scholar

[22] D. L. Johnson and H. Mawdesley, Some groups of Fibonacci type, J. Aust. Math. Soc. 20 (1975), no. 2, 199–204. 10.1017/S1446788700020498Search in Google Scholar

[23] D. L. Johnson, J. W. Wamsley and D. Wright, The Fibonacci groups, Proc. Lond. Math. Soc. (3) 29 (1974), 577–592. 10.1112/plms/s3-29.4.577Search in Google Scholar

[24] J. Lin and S. Wang, Fixed subgroups of automorphisms of hyperbolic 3-manifold groups, Topology Appl. 173 (2014), 175–187. 10.1016/j.topol.2014.05.020Search in Google Scholar

[25] C. Maclachlan, Generalisations of Fibonacci numbers, groups and manifolds, Combinatorial and Geometric Group Theory (Edinburgh 1993), London Math. Soc. Lecture Note Ser. 204, Cambridge University, Cambridge (1995), 233–238. 10.1017/CBO9780511566073.017Search in Google Scholar

[26] W. Magnus, Noneuclidean Tesselations and Their Groups, Pure Appl. Math. 61, Academic Press, New York, 1974. Search in Google Scholar

[27] K. McDermott, On the topology of the groups of type ℨ, Topology Appl. 307 (2022), Paper No. 107767. 10.1016/j.topol.2021.107767Search in Google Scholar

[28] M. Merzenich, A computational method for building spherical pictures and theoretic results from explicit constructions, PhD thesis, Oregon State University, 2020. Search in Google Scholar

[29] R. V. Moody, B. Jessen, J. Brillhart, A. Sutcliffe, D. J. Newman, C. S. Venkataraman, R. Sivaramakrishnan, J. H. Conway and L. Flatto, Problems and solutions: Advanced problems: 5320-5329, Amer. Math. Monthly 72 (1965), no. 8, 914–915. 10.2307/2315058Search in Google Scholar

[30] F. Parker, forrestwparker/tools-for-cyclically-presented-groups: Initial documentation, Zenodo, 2017. Search in Google Scholar

[31] A. J. Sieradski, Combinatorial squashings, 3-manifolds, and the third homology of groups, Invent. Math. 84 (1986), no. 1, 121–139. 10.1007/BF01388735Search in Google Scholar

[32] A. J. Sieradski, Algebraic topology for two-dimensional complexes, Two-Dimensional Homotopy and Combinatorial Group Theory, London Math. Soc. Lecture Note Ser. 197, Cambridge University, Cambridge (1993), 51–96. 10.1017/CBO9780511629358.004Search in Google Scholar

[33] R. M. Thomas, On a question of Kim concerning certain group presentations, Bull. Korean Math. Soc. 28 (1991), no. 2, 219–224. Search in Google Scholar

[34] R. M. Thomas, The Fibonacci groups revisited, Groups—St. Andrews 1989, Vol. 2, London Math. Soc. Lecture Note Ser. 160, Cambridge University, Cambridge (1991), 445–454. 10.1017/CBO9780511661846.017Search in Google Scholar

[35] G. Williams, The aspherical Cavicchioli–Hegenbarth–Repovš generalized Fibonacci groups, J. Group Theory 12 (2009), no. 1, 139–149. 10.1515/JGT.2008.066Search in Google Scholar

[36] G. Williams, Unimodular integer circulants associated with trinomials, Int. J. Number Theory 6 (2010), no. 4, 869–876. 10.1142/S1793042110003289Search in Google Scholar

[37] G. Williams, Groups of Fibonacci type revisited, Internat. J. Algebra Comput. 22 (2012), no. 8, Article ID 1240002. 10.1142/S0218196712400024Search in Google Scholar

[38] The GAP Group, GAP – Groups, Algorithms, and Programming, version 4.11.1, 2021. Search in Google Scholar