Notes on 3-Manifolds
These notes were an ambitious attempt to summarize and restate in my own words the major introductory results in 3-manifold theory. The introduction was to be a brief review of requisite material learned in my first two years of studying topology. Chapter 2 was to utilize the duality of 1-handles and 2-handles in 3-dimensions to prove the Poincare Duality Theorem. (I would still love to revisit this). The next chapters are my understanding of Chapters 1 and 2 of Hatchers 3-Manifolds notes. The section that proves the Loop Theorem is a combination of Jaco’s and Hatcher’s treatments. The blank section Loop Theorem (Hierarchy Construction) was to cover Lackenby’s proof of the Loop Theorem using Haken’s idea of Hierarchies. This is still something I would like to add!
These notes were an ambitious attempt to summarize and restate in my own words the major introductory results in 3-manifold theory. The introduction was to be a brief review of requisite material learned in my first two years of studying topology. Chapter 2 was to utilize the duality of 1-handles and 2-handles in 3-dimensions to prove the Poincare Duality Theorem. (I would still love to revisit this). The next chapters are my understanding of Chapters 1 and 2 of Hatchers 3-Manifolds notes. The section that proves the Loop Theorem is a combination of Jaco’s and Hatcher’s treatments. The blank section Loop Theorem (Hierarchy Construction) was to cover Lackenby’s proof of the Loop Theorem using Haken’s idea of Hierarchies. This is still something I would like to add!