Title: Willis Theory via Graphs,
Abstract: We study the scale and tidy subgroups of an endomorphism of a totally
disconnected locally compact group using a geometric framework. This leads to
new interpretations of tidy subgroups and the scale function. Foremost, we
obtain a geometric tidying procedure which applies to endomorphisms as well as
a geometric proof of the fact that tidiness is equivalent to being minimizing
for a given endomorphism. Our framework also yields an endomorphism version of
the Baumgartner-Willis tree representation theorem. We conclude with a
construction of new endomorphisms of totally disconnected locally compact
groups from old via HNN-extensions.