# 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.

*For More Information:* craigw@ms.unimelb.edu.au