Coarse equivalence and topological couplings of locally compact groups
M. Gromov has shown that any two finitely generated groups $$\Gamma $$Γ and $$\Lambda $$Λ are quasi-isometric if and only if they admit a topological coupling, i.e., a commuting pair of proper continuous cocompact actions $$\Gamma \curvearrowright X \curvearrowleft \Lambda $$Γ↷X↶Λ on a locally compact Hausdorff space. This result is extended here to all (compactly generated) locally compact second-countable groups.
MEASURE EQUIVALENCE FOR NON-UNIMODULAR GROUPS
We undertake a comprehensive study of measure equivalence between general locally compact, second countable groups, providing operator algebraic and ergodic theoretic reformulations, and complete the classification of amenable groups within this class up to measure equivalence.
Athenian Democracy at War
Classical Athens perfected direct democracy. The plays of this ancient Greek state are still staged today. These achievements are rightly revered. Less well known is the other side of this success story. Democratic Athens completely transformed warfare and became a superpower. The Athenian armed forces were unmatched in size and professionalism. This book explores the major reasons behind this military success. It shows how democracy helped the Athenians to be better soldiers. For the first time David M. Pritchard studies, together, all four branches of the armed forces. He focuses on the background of those who fought Athens' wars and on what they thought about doing so. His book reveals the common practices that Athens used right across the armed forces and shows how Athens' pro-war culture had a big impact on civilian life. The book puts the study of Athenian democracy at war on an entirely new footing.