  We use the framework of matrix factorizations to study topological B-type
D-branes on the cubic curve. Specifically, we elucidate how the brane RR
charges are encoded in the matrix factors, by analyzing their structure in
terms of sections of vector bundles in conjunction with equivariant R-symmetry.
One particular advantage of matrix factorizations is that explicit moduli
dependence is built in, thus giving us full control over the open-string moduli
space. It allows one to study phenomena like discontinuous jumps of the
cohomology over the moduli space, as well as formation of bound states at
threshold. One interesting aspect is that certain gauge symmetries inherent to
the matrix formulation lead to a non-trivial global structure of the moduli
space. We also investigate topological tachyon condensation, which enables us
to construct, in a systematic fashion, higher-dimensional matrix factorizations
out of smaller ones; this amounts to obtaining branes with higher RR charges as
composites of ones with minimal charges. As an application, we explicitly
construct all rank-two matrix factorizations.
