To modify the shape of a single edge, the topology.ST_ChangeEdgeGeom function is used. There are three arguments to supply: the topology name, the edge ID, and the new geometry. For example, we'll modify the border between East and West Neverland: the edge with an ID of 4778:

SELECT topology.ST_ChangeEdgeGeom('my_topology',4778,'SRID=4326;LINESTRING(-2 0.00099999999999989, -1.75 0.1, -1.5 0.001)'); 

Note that there's no tolerance, and the start and end points must precisely match. It's best to derive the first and last points for a new geometry from an existing geometry.

This is where PostGIS topology really shines: the geometry is changed once and only once, and both polygons will be still perfectly adjacent.