
Sheaves on Graphs and a Proof of the Hanna Neumann Conjecture
Note:
Here
is a remarkable and much shorter
proof of the Hanna Neumann Conjecture,
which simplifies, generalizes, and clarifies aspects of
my sheaf theoretic proof,
by Warren Dicks, written entirely in the language of skew group rings.
remarkable simplifications, by Warren Dicks.
You may want to read Dicks' version before mine...
 Postscript version.
 Dvi version.
 PDF version.

Abstract:
The main goal of this paper is to prove the Hanna Neumann Conjecture;
in fact, we prove a strengthened form of the conjecture.
We study these conjectures using
what we have
called ``sheaves on graphs'' in \cite{friedman_sheaves}. We show
that both conjectures are implied by the vanishing of a certain invariant,
the ``maximum excess,'' of certain sheaves that we call
$\rho$kernels.
Our approach involves ``graph Galois theory,'' an analogue of classical
Galois theory in the graph setting. We use it to construct
the $\rho$kernels.
We use the symmetry in Galois theory to argue that if the
Strengthened Hanna Neumann Conjecture is false, then the maximum excess
of ``most of'' these $\rho$kernels must be large.
We then give an inductive argument to show that this is impossible.
