arXiv:1501.04313 Abstract | arXiv Analytics

arXiv:1501.04313 [math.GR]Abstract References Reviews Resources

Thompson's group F is 1-counter graph automatic

Published 2015-01-18Version 1

It is not known whether Thompson's group F is automatic. With the recent extensions of the notion of an automatic group to graph automatic by Kharlampovich, Khoussainov and Miasnikov and then to C-graph automatic by the authors, a compelling question is whether F is graph automatic or C-graph automatic for an appropriate language class C. The extended definitions allow the use of a symbol alphabet for the normal form language, replacing the dependence on generating set. In this paper we construct a 1-counter graph automatic structure for F based on the standard infinite normal form for group elements.

Categories: math.GR

Subjects: 20F65, 68Q45

Keywords: thompsons group, c-graph automatic, standard infinite normal form, appropriate language class, normal form language

Related articles: Most relevant | Search more

arXiv:1107.0672 [math.GR] (Published 2011-07-04, updated 2011-09-12)

Centralizers in R. Thompson's group V_n

Collin Bleak, Hannah Bowman, Alison Gordon, Garrett Graham, Jacob Hughes, Francesco Matucci, Jenya Sapir

arXiv:math/0208117 [math.GR] (Published 2002-08-14)

Combinatorial properties of Thompson's group F

Sean Cleary, Jennifer Taback

arXiv:1501.06682 [math.GR] (Published 2015-01-27)

The $Σ$-invariants of Thompson's group $F$ via Morse theory