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

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

Reflex impairment as a measure of vitality and survival potential of Atlantic cod (Gadus morhua)

A ssur ing the v itality and survival potential of live-caught Atlantic cod (Gadus morhua) is important for improving the sorting of fish before net penning operations designed to hold fish for growth and later market. When Atlantic cod are captured by Danish seine, the most commonly used fishing gear for live-caught fish, they undergo stressors such as forced swimming, net abrasion, and air exposure. Laboratory experiments (at an air temperature of 9°C and water temperature of 8°C) were conducted with the aim of constructing a RAMP (reflex action mortality predictor) curve for prediction of vitality and survival potential in Atlantic cod captured in Danish seines, by varying the levels of these stressors. Atlantic cod exposed to increased duration in air (5–20 min) showed increased reflex impairment and mortality, with 75% mortality at 10 minutes of air exposure. Forced swimming in combination with net abrasion and air exposure did not increase reflex impairment or mortality above that associated with air exposure alone. The Atlantic cod RAMP curves indicated that fish with reflex impairment less than 50% would not show mortality and would likely recover from capture stress