# Finding non-trivial splittings in groups, and similar results in geometry

Algebra/Geometry/Topology Seminar

#### by Maurice Chiodo

Institution: U. Melbourne
Date: Tue 1st June 2010
Time: 2:15 PM
Location: Doug McDonell 309

Abstract: It is well known that there is no algorithm to decide if a finitely presented group splits as a non-trivial free product, nor is there an algorithm to decide if a closed 4-manifold can be written as a connect sum of two non simply connected summands. In this talk I will show that, even if we know that a given finitely presented group splits as a non-trivial free product, we cannot always algorithmically split it. I will use this to show an analogous result in geometry: even if we know that a given closed 4-manifold splits as a connect sum of two non simply connected summands, we cannot always algorithmically split it.