The large scale geometry of strongly aperiodic subshifts of finite type

A subshift on a group G is a closed, G-invariant subset of A^G, for some finite set A. It is said to be a subshift of finite type (SFT) if it is defined by a finite collection of 'forbidden patterns', to be strongly aperiodic if all point stabilizers are trivial, and weakly aperiodic if all point stabilizers are infinite index in G. We show that groups with at least 2 ends have a strongly aperiodic SFT, and that having such an SFT is a QI invariant for finitely presented torsion free groups. We show that a finitely presented torsion free group with no weakly aperiodic SFT must be QI-rigid. The domino problem on G asks whether the SFT specified by a given set of forbidden patterns is empty. We show that decidability of the domino problem is a QI invariant.Comment: 23 pages, 6 figures. The proof of the main theorem has been simplified and some new corollaries deduce

X-Rays From Magnetically Channeled Winds Of OB Stars, In \u27Magnetic Massive Stars\u27

OB stars with strong radiation-driven stellar winds and large-scale magnetic fields generate strong and hard X-ray emission via the Magnetically Channeled Wind Shock (MCWS) mechanism. In this brief paper, I describe four separate X-ray diagnostics of the MCWS mechanism in OB stars, with applications to the prototype young O star, theta-1 Ori C