Jul 2013

A Topological Splitting Theorem for Poincare Duality Groups and High-dimensional Manifolds

My paper with Aditi Kar has appeared at Geometry & Topology 17 (2013) 2203–2221, DOI: 10.2140/gt.2013.17.2203.

We show that for a wide class of manifold pairs N,M with dim(M) = dim(N) + 1, every π1–injective map f : N M factorises up to homotopy as a finite cover of an embedding. This result, in the spirit of Waldhausen’s torus theorem, is derived using Cappell’s surgery methods from a new algebraic splitting theorem for Poincaré duality groups. As an application we derive a new obstruction to the existence of π1–injective maps.