arXiv 0905.37812009-05math.GRmath.CO

加强的Hanna Neumann猜想的一个证明

A Proof of the Strengthened Hanna Neumann Conjecture

Joel Friedman

备注：: This paper was been withdrawn by the author due to a crucial error in thinking that it is immediate that the vanishing of rho kernels of a direct sum of sheaves is equivalent to the individual vanishing. A corrected version of the proof is available as "The Strengthened Hanna Neumann Conjecture I", which gives a proof without sheaf theory (really translating the sheaf theory to combinatorics). A sequel to this paper, "The Strengthened Hanna Neumann Conjecture II" is in preparation; this will develop sheaf theory and give a simple proof of the conjecture (simple assuming the sheaf theory is in place).

摘要：

证明了Hanna Neumann猜想。我们给出了一个更直接的上同调解释的猜想的“典型”覆盖映射，并使用图伽罗瓦论“对称化”的猜想。该猜想则与层态射的某个核有关，并且只要这些核在覆盖上同调理论中是余非循环的，该猜想就被隐含了。这使我们能够证明一个稍微广义的加强汉娜诺依曼猜想;这个猜想是假的，如果推广到所有层。我们所使用的核在图论中并不存在，所以我们使用层理论似乎对这种方法至关重要。

英文摘要：

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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摘要：

英文摘要：

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