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Virtual geometricity is rare. (English) Zbl 1362.20022

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.

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
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