论文信息 - Aperiodic Subshifts on Polycyclic Groups

Aperiodic Subshifts on Polycyclic Groups

We prove that every polycyclic group of nonlinear growth admits a strongly aperiodic SFT and has an undecidable domino problem. This answers a question of [4] and generalizes the result of [2].

Emmanuel Jeandel | E. Jeandel

[1] A. Penland,et al. Periodic Points on Shifts of Finite Type and Commensurability Invariants of Groups , 2015, 1502.03195.

[2] Robert L. Berger. The undecidability of the domino problem , 1966 .

[3] Emmanuel Jeandel. Some Notes about Subshifts on Groups , 2015, ArXiv.

[4] Alexis Ballier,et al. The domino problem on groups of polynomial growth , 2013, 1311.4222.

[5] Douglas Lind,et al. An Introduction to Symbolic Dynamics and Coding , 1995 .

[6] Markus Lohrey,et al. Logical aspects of Cayley-graphs: the group case , 2005, Ann. Pure Appl. Log..

[7] Jarkko Kari,et al. A small aperiodic set of Wang tiles , 1996, Discret. Math..

[8] Jarkko Kari,et al. An Aperiodic Set of Wang Cubes , 1996, J. Univers. Comput. Sci..

[9] Gilbert Baumslag,et al. Algorithmically insoluble problems about finitely presented solvable groups, lie, and associative algebras , 1985 .

[10] David Bruce Cohen,et al. The large scale geometry of strongly aperiodic subshifts of finite type , 2014, 1412.4572.

[11] Jarkko Kari,et al. Tiling Problems on Baumslag-Solitar groups , 2013, MCU.