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 and coarse equivalence for unimodular locally compact groups
This article is concerned with measure equivalence and uniform measure equivalence of locally compact, second countable groups. We show that two unimodular, locally compact, second countable groups are measure equivalent if and only if they admit free, ergodic, probability measure preserving actions whose cross section equivalence relations are stably orbit equivalent. Using this we prove that in the presence of amenability any two such groups are measure equivalent and that both amenability and property (T) are preserved under measure equivalence, extending results of Connes-Feldman-Weiss and Furman. Furthermore, we introduce a notion of uniform measure equivalence for unimodular, locally compact, second countable groups, and prove that under the additional assumption of amenability this notion coincides with coarse equivalence, generalizing results of Shalom and Sauer. Throughout the article we rigorously treat measure theoretic issues arising in the setting of non-discrete groups.
American Insurgents, American Patriots: The Revolution of the People
This is a story of rumour, charity, vengeance, and restraint. "American Insurgents, American Patriots" reminds us that revolutions are violent events. They provoke passion and rage, a willingness to use violence to achieve political ends, a deep sense of betrayal, and a strong religious conviction that God expects an oppressed people to defend their rights. The American Revolution was no exception. A few celebrated figures in the Continental Congress do not make for a revolution. It requires tens of thousands of ordinary men and women willing to sacrifice, kill, and be killed. Breen not only tells the history of these ordinary Americans but, drawing upon a wealth of rarely seen documents, restores their primacy to America's road to independence. Mobilizing two years before the Declaration of Independence, American insurgents in all thirteen colonies concluded that resistance to British oppression required organized violence against the state. They channeled popular rage through elected committees of safety and observation, which before 1776 were the heart of American resistance. "American Insurgents, American Patriots" is the stunning account of their insurgency, without which there would have been no independent republic as we know it.