TopologyExceptions are thrown when the topological graph GEOS uses to compute relationships enters an invalid or impossible state.  There are two reasons for TopologyExceptions to be thrown:

* GEOS is handling a valid geometry case incorrectly. That is, a '''bug'''.
* GEOS is handling an invalid geometry case correctly. 

Before submitting a bug ticket based on a TopologyException, ensure your geometries are valid, by running the IsValid method on them.  In PostGIS, the ST_IsValid() function calls the appropriate GEOS test.  If your geometries are invalid, the problem is with your geometry, not with GEOS.