1Justus-Liebig Universität Giessen, Germany 2Steklov Mathematical Institute of Russian Academy of Sciences; National Research University Higher School of Economics, Moscow, Russia
Groups, geometry, and dynamics, Tome 12 (2018) no. 4, pp. 1485-1521
We study counting functions on the free groups Fn and free monoids Mn for n≥2, which we introduce for combinatorial approach to famous Brooks quasimorphisms on free groups. Two counting functions are considered equivalent if they differ by a bounded function. We find the complete set of linear relations between equivalence classes of counting functions and apply this result to construct an explicit basis for the vector space of such equivalence classes. Moreover, we provide a simple graphical algorithm to determine whether two given counting functions are equivalent. In particular, this yields an algorithm to decide whether two linear combinations of Brooks quasimorphisms on Fn represent the same class in bounded cohomology.
1
Justus-Liebig Universität Giessen, Germany
2
Steklov Mathematical Institute of Russian Academy of Sciences; National Research University Higher School of Economics, Moscow, Russia
Tobias Hartnick; Alexey Talambutsa. Relations between counting functions on free groups and free monoids. Groups, geometry, and dynamics, Tome 12 (2018) no. 4, pp. 1485-1521. doi: 10.4171/ggd/476
@article{10_4171_ggd_476,
author = {Tobias Hartnick and Alexey Talambutsa},
title = {Relations between counting functions on free groups and free monoids},
journal = {Groups, geometry, and dynamics},
pages = {1485--1521},
year = {2018},
volume = {12},
number = {4},
doi = {10.4171/ggd/476},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/476/}
}
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AU - Alexey Talambutsa
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