The tangential end fibration of an aspherical Poincare complex

Abstract

We construct a sphere fibration over a finite aspherical Poincare complex X, which we call the tangential end fibration, under the condition that the universal cover of X is forward tame and simply connected at infinity. We show that it is tangent to X if the formal dimension of X is even or, when the formal dimension is odd, if the diagonal X -> X x X admits a Poincare embedding structure. (C) 2007 Elsevier Ltd. All rights reserved.