  More than two decades ago, combinatorial topology was shown to be useful for
analyzing distributed fault-tolerant algorithms in shared memory systems and in
message passing systems. In this work, we show that combinatorial topology can
also be useful for analyzing distributed algorithms in failure-free networks of
arbitrary structure. To illustrate this, we analyze consensus, set-agreement,
and approximate agreement in networks, and derive lower bounds for these
problems under classical computational settings, such as the LOCAL model and
dynamic networks.
