  We give a topological characterisation of alternating knot exteriors based on
the presence of special spanning surfaces. This shows that alternating is a
topological property of the knot exterior and not just a property of diagrams,
answering an old question of Fox. We also give a characterisation of
alternating link exteriors which have marked meridians. We then describe a
normal surface algorithm which can decide if a knot is prime and alternating
given a triangulation of its exterior as input.
