Copies of the classnotes are on the internet in PDF format as given below. The "Proofs of Theorems" files were prepared in Beamer. The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses. These notes and supplements have not been classroom tested (and so may have some typographical errors).

Topology 2 (MATH 5360) at the graduate level is not a formal class at ETSU. Such a class existed previously when ETSU was still on the quater system, but ultimately the topology classes were all merged into the undergraduate/graduate cross-listed class Introduction to Topology (MATH 4357/5357) in the late 1990s. The prerequisite for Topology 2 is Topology 1 (MATH 5350). Online notes for are available for Introduction to Topology: General Topology and Introduction to Topology: Algebraic Topology (based on James Munkres' Topology, 2nd Edition), and Topology 1 (based on Glen Bredon's Topology and Geometry). Topology 2 covers Chapter V (Cohomology), Chapter VI (Products and Duality), and Chapter VII (Homotopy Theory).

• Chapter V. Cohomology.
• Chapter VI. Products and Duality.
• Chapter VII. Homotopy Theory.

Chapter V. Cohomology.

• Section V.1. Multilinear Algebra.
• Section V.2. Differential Forms.
• Section V.3. Integration of Forms.
• Section V.4. Stokes' Theorem.
• Section V.5. Relationship to Singular Homology.
• Section V.6. More Homological Algebra.
• Section V.7. Universal Coefficient Theorems.
• Section V.8. Excision and Homotopy.
• Section V.9. de Rham's Theorem.
• Section V.10. The de Rham Theory of CPⁿ.
• Section V.11. Hopf's Theorem on Maps to Spheres.
• Section V.12. Differential Forms on Compact Lie Groups.
• Study Guide V.

Chapter VI. Products and Duality.

• Section VI.1. The Cross Product and the Kiinneth Theorem.
• Section VI.2. A Sign Convention.
• Section VI.3. The Cohomology Cross Product.
• Section VI.4. The Cup Product.
• Section VI.5. The Cap Product.
• Section VI.6. Classical Outlook on Duality.
• Section VI.7. The Orientation Bundle.
• Section VI.8. Duality Theorems.
• Section VI.9. Duality on Compact Manifolds with Boundary.
• Section VI.10. Applications of Duality.
• Section VI.11. Intersection Theory.
• Section VI.12. The Euler Class, Lefschetz Numbers, and Vector Fields.
• Section VI.13. The Gysin Sequence.
• Section VI.14. Lefschetz Coincidence Theory.
• Section VI.15. Steenrod Operations.
• Section VI.16. Construction of the Steenrod Squares.
• Section VI.17. Stiefel-Whitney Classes.
• Section VI.18. Plumbing.
• Study Guide VI.

Chapter VII. Homotopy Theory.

• Section VII.1. Colibrations.
• Section VII.2. The Compact-Open Topology.
• Section VII.3. H-Spaces, H-Groups, and H-Cogroups.
• Section VII.4. Homotopy Groups.
• Section VII.5. The Homotopy Sequence of a Pair.
• Section VII.6. Fiber Spaces.
• Section VII.7. Free Homotopy.
• Section VII.8. Classical Groups and Associated Manifolds.
• Section VII.9. The Homotopy Addition Theorem.
• Section VII.10. The Hurewicz Theorem.
• Section VII.11. The Whitehead Theorem.
• Section VII.12. Eilenberg-Mac Lane Spaces.
• Section VII.13. Obstruction Theory.
• Study Guide VII.

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