Units Unit 0: Introduction Unit 1: Gauss Bonnet Unit 2: Poincare Hopf Unit 3: Index expectation Unit 4: Euler's Gem Unit 5: Euler Poincare Unit 6: Unimodularity Unit 7: Brouwer Lefschetz Unit 8: Sphere formula Unit 9: Level sets Unit 10: Index formula Unit 11: Quadratic cohomology Unit 12: Higher Green

Footnotes and References Footnotes Videos Topics in Geometry Playlist Appendices Appendix 0: Graphs Appendix 1: Sets Appendix 2: Complexes Appendix 3: Linear algebra Appendix 4: Topology Appendix 5: Homotopy Appendix 6: Calculus

July 31:

A snapshot document 63 pages, July 31, 2026

July 18: A theorem which fell off as a low hanging fruit by combining a few of the above theorems: