  In the renaming problem, each process in a distributed system is issued a
unique name from a large name space, and the processes must coordinate with one
another to choose unique names from a much smaller name space. We show that
lower bounds on the solvability of renaming in an asynchronous distributed
system can be formulated as a purely topological question about the existence
of an equivariant chain map from a topological disk to a topological annulus.
Proving the non-existence of such a map implies the non-existence of a
distributed renaming algorithm in several related models of computation.
