  In this paper, we show that simple, thick negatively curved two-dimensional
P-manifolds, a large class of surface amalgams, are marked length spectrum
rigid. That is, if two piecewise negatively curved Riemannian metrics
(satisfying certain smoothness conditions) on a simple, thick two-dimensional
P-manifold assign the same lengths to all closed geodesics, then they differ by
an isometry up to isotopy. Our main theorem is a natural generalization of
Croke and Otal's celebrated results about marked length spectrum rigidity of
negatively curved surfaces.
