Cashen, Christopher H.; Manning, Jason F. Virtual geometricity is rare. (English) Zbl 1362.20022 LMS J. Comput. Math. 18, 444-455 (2015). Summary: We present the results of computer experiments suggesting that the probability that a random multiword in a free group is virtually geometric decays to zero exponentially quickly in the length of the multiword. We also prove this fact. Cited in 6 Documents MSC: 20E05 Free nonabelian groups 20P05 Probabilistic methods in group theory 57M10 Covering spaces and low-dimensional topology 57M05 Fundamental group, presentations, free differential calculus Keywords:virtual geometricity; random multiword; free group PDFBibTeX XMLCite \textit{C. H. Cashen} and \textit{J. F. Manning}, LMS J. Comput. Math. 18, 444--455 (2015; Zbl 1362.20022) Full Text: DOI arXiv References: [1] DOI: 10.4310/MRL.1997.v4.n2.a3 · Zbl 0983.20023 · doi:10.4310/MRL.1997.v4.n2.a3 [2] DOI: 10.2307/1968618 · Zbl 0015.24804 · doi:10.2307/1968618 [3] DOI: 10.1142/S0218196711006741 · Zbl 1242.20053 · doi:10.1142/S0218196711006741 [4] DOI: 10.1112/jlms/s2-17.3.555 · Zbl 0412.57006 · doi:10.1112/jlms/s2-17.3.555 [5] DOI: 10.1109/MCSE.2007.53 · Zbl 05333419 · doi:10.1109/MCSE.2007.53 [6] DOI: 10.2307/1970113 · Zbl 0078.16402 · doi:10.2307/1970113 [7] Gromov, Geometric group theory, Vol. 2 (Sussex, 1991) 182 pp 1– (1993) · Zbl 0820.53035 [8] DOI: 10.1112/jlms/s2-46.1.123 · Zbl 0797.20030 · doi:10.1112/jlms/s2-46.1.123 [9] DOI: 10.1007/BF02471762 · Zbl 0949.20033 · doi:10.1007/BF02471762 [10] DOI: 10.4310/MRL.2010.v17.n5.a9 · Zbl 1236.20029 · doi:10.4310/MRL.2010.v17.n5.a9 [11] DOI: 10.1112/jlms/jdq007 · Zbl 1205.20049 · doi:10.1112/jlms/jdq007 [12] DOI: 10.1007/s00039-012-0153-z · Zbl 1280.20044 · doi:10.1007/s00039-012-0153-z [13] DOI: 10.1017/CBO9780511626302 · Zbl 1106.37301 · doi:10.1017/CBO9780511626302 [14] DOI: 10.2140/pjm.2006.223.113 · Zbl 1149.20028 · doi:10.2140/pjm.2006.223.113 [15] DOI: 10.1007/s00039-009-0041-3 · Zbl 1242.20052 · doi:10.1007/s00039-009-0041-3 [16] DOI: 10.2140/gt.2011.15.1419 · Zbl 1272.20046 · doi:10.2140/gt.2011.15.1419 [17] DOI: 10.1007/s000140050047 · Zbl 0979.20026 · doi:10.1007/s000140050047 [18] DOI: 10.4213/mzm1744 · doi:10.4213/mzm1744 [19] Stallings, Geometric group theory down under (Canberra, 1996) pp 317– (1999) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.