  In an earlier paper (math.SG/0110169), we introduced absolute gradings on the
three-manifold invariants developed in math.SG/0101206 and math.SG/0105202.
Coupled with the surgery long exact sequences, we obtain a number of three- and
four-dimensional applications of this absolute grading including strengthenings
of the ``complexity bounds'' (from math.SG/0101206), restrictions on knots
whose surgeries give rise to lens spaces, and calculations of $\HFp$ for a
variety of three-manifolds. Moreover, we show how the structure of $\HFp$
constrains the exoticness of definite intersection forms for smooth
four-manifolds which bound a given three-manifold. In addition to these new
applications, the techniques also provide alternate proofs of Donaldson's
diagonalizability theorem and the Thom conjecture for $\CP{2}$.
