A Proof of the Strengthened Hanna Neumann Conjecture

Details A Proof of the Strengthened Hanna Neumann Conjecture A Proof of the Strengthened Hanna Neumann Conjecture

2009-05-23

arxiv.org/abs/0905.3781v2

Mathematics

Group Theory

This paper was been withdrawn by the author due to a crucial error in thinking that it is immediate that the vanishing of rho

Scientific paper

We prove the Strengthened Hanna Neumann Conjecture. We give a more direct cohomological interpretation of the conjecture in terms of "typical" covering maps, and use graph Galois theory to "symmetrize" the conjecture. The conjecture is then related to certain kernel of a morphism of sheaves, and is implied provided these kernels are co-acyclic in the covering cohomology theory. This allows us to prove a slightly generalized Strengthened Hanna Neumann Conjecture; this conjecture is false if generalized to all sheaves. The kernels we use do not exist in the theory of graphs, so our use of sheaf theory seems essential to this approach.

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