Sheaves on Graphs, Their Homological Invariants, and a Proof of the Hanna Neumann Conjecture.

Cover -- Title page -- Preface -- Introduction -- Chapter 1. Foundations of Sheaves on Graphs and Their Homological Invariants -- 1.1. Introduction -- 1.2. Basic Definitions and Main Results -- 1.3. Galois and Covering Theory -- 1.4. Sheaf Theory and Homology -- 1.5. Twisted Cohomology -- 1.6. Maximum Excess and Supermodularity -- 1.7. ℎ₁^{ } and the Universal Abelian Covering -- 1.8. Proof of Theorem 1.10 -- 1.9. Concluding Remarks -- Chapter 2. The Hanna Neumann Conjecture -- 2.1. Introduction -- 2.2. The Strengthened Hanna Neumann Conjecture -- 2.3. Graph Theoretic Formulation of the SHNC -- 2.4. Galois and Covering Theory in the SHNC -- 2.5. -kernels -- 2.6. Symmetry and Algebra of the Excess -- 2.7. Variability of -th Power Kernels -- 2.8. Proof of the SHNC -- 2.9. Concluding Remarks -- Appendix A. A Direct View of -Kernels -- Appendix B. Joel Friedman's Proof of the strengthened Hanna Neumann conjecture by Warren Dicks -- B.1. Sheaves on graphs -- B.2. Free groups and graphs -- B.3. The strengthened Hanna Neumann conjecture -- Bibliography -- Back Cover.

In this paper the author establishes some foundations regarding sheaves of vector spaces on graphs and their invariants, such as homology groups and their limits. He then uses these ideas to prove the Hanna Neumann Conjecture of the 1950s; in fact, he proves a strengthened form of the conjecture.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.