When are two Coxeter orbifolds diffeomorphic?

One can define what it means for a compact manifold with corners to be a "contractible manifold with contractible faces." Two combinatorially equivalent, contractible manifolds with contractible faces are diffeomorphic if and only if their 4-dimensional faces are diffeomorphic. It follows that two simple convex polytopes are combinatorially equivalent if and only if they are diffeomorphic as manifolds with corners. On the other hand, by a result of Akbulut, for each n > 3, there are smooth, contractible n-manifolds with contractible faces which are combinatorially equivalent but not diffeomorphic. Applications are given to rigidity questions for reflection groups and smooth torus actions.Comment: 24 page

The Euler characteristic of a polyhedral product

Given a finite simplicial complex L and a collection of pairs of spaces indexed by its vertex set, one can define their polyhedral product. We record a simple formula for its Euler characteristic. In special cases the formula simplifies further to one involving the h-polynomial of L.Comment: 5 page

Random graph products of finite groups are rational duality groups

Given an edge-independent random graph G(n,p), we determine various facts about the cohomology of graph products of groups for the graph G(n,p). In particular, the random graph product of a sequence of finite groups is a rational duality group with probability tending to 1 as n goes to infinity. This includes random right angled Coxeter groups as a special case.Comment: 29 page

Cohomology of Coxeter groups with group ring coefficients: II

For any Coxeter group W, we define a filtration of H^*(W;ZW) by W-submodules and then compute the associated graded terms. More generally, if U is a CW complex on which W acts as a reflection group we compute the associated graded terms for H_*(U) and, in the case where the action is proper and cocompact, for H^*_c(U).Comment: This is the version published by Algebraic & Geometric Topology on 15 September 200

Race and Policing: An Agenda for Action

This paper is organized into two parts -- Strategic Voice and Tactical Agency. Strategic Voice argues that problems of race in policing cannot be resolved by the police alone. Other people must help by understanding and ameliorating the social conditions that cause race to be associated with crime and hence become a dilemma for American policing. Rather than accepting these conditions as givens, police leaders with their powerful collective voice should actively call attention to what needs to be changed. Tactical Agency outlines what the police can do on their own initiative to deal with the operational dilemmas of race -- in the communities they serve and in their own organizations

Escaping the \u3cem\u3eSporhase\u3c/em\u3e Maze: Protecting State Waters within the Commerce Clause

Eastern states, though they have enjoyed a history of relatively abundant water, increasingly face the need to conserve water, particularly to protect water-dependent ecosystems. At the same time, growing water demands, climate change, and an emerging water-oriented economy have intensified pressure for interstate water transfers. Thus, even traditionally wet states are seeking to protect or secure their water supplies. However, restrictions on water sales and exports risk running afoul of the Dormant Commerce Clause. This Article offers guidance for states, partciularly eastern states concerned with maintaining and improving water-dependent ecosystems, in seeking to restrict water exports while staying within the confines of the Dormant Commerce Clause