  Bordered Heegaard Floer homology is an invariant for 3-manifolds, which
associates to a surface F an algebra A(Z), and to a 3-manifold Y with boundary,
together with an orientation-preserving diffeomorphism \phi from F to \bdy Y, a
module over A(Z). We study the Grothendieck group of modules over A(Z), and
define an invariant lying in this group for every bordered 3-manifold. We prove
that this invariant recovers the kernel of the inclusion of H_1(\bdy Y; Z) into
H_1(Y; Z) if H_1(Y, \bdy Y; Z) is finite, and is 0 otherwise. We also study the
properties of this invariant corresponding to gluing. As one application, we
show that the pairing theorem for bordered Floer homology categorifies the
classical Alexander polynomial formula for satellites.
