We give results on reduced complex-analytic curve germs which relate their indecomposable maximal Cohen-Macaulay (MCM) modules to their lattice homology groups and related invariants, thereby providing a connection between the algebraic theory of MCM modules and techniques arising from low-dimensional topology. In particular, we characterize the germs (C, o) of finite Cohen-Macaulay type in terms of the lattice homology H_* (C, o), and those of tame type in terms of the lattice homologies and associated spectral sequences of (C, o) and its subcurves, including the distinction between germs of finite and infinite growth. As a consequence of these results, we obtain corresponding characterizations of a germ's Cohen-Macaulay type in terms of the motivic Poincaré series.
Hof et al. (Mon,) studied this question.