Lecture Notes

These lecture notes are based on a live LaTeX record made by Sanath Devalapurkar with images by Xianglong Ni, both of whom were students in the class at the time it was taught on campus.

LEC # LECTURE NOTES
I. Singular Homology
1 This resource may not render correctly in a screen reader.Introduction: Singular Simplices and Chains (PDF)
2 This resource may not render correctly in a screen reader.Homology (PDF)
3 This resource may not render correctly in a screen reader.Categories, Functors, Natural Transformations (PDF)
4 This resource may not render correctly in a screen reader.Categorical Language (PDF)
5 This resource may not render correctly in a screen reader.Homotopy, Star-shaped Regions (PDF)
6 This resource may not render correctly in a screen reader.Homotopy Invariance of Homology (PDF)
7 This resource may not render correctly in a screen reader.Homology Cross Product (PDF)
8 This resource may not render correctly in a screen reader.Relative Homology (PDF)
9 This resource may not render correctly in a screen reader.The Homology Long Exact Sequence (PDF)
10 This resource may not render correctly in a screen reader.Excision and Applications (PDF)
11 This resource may not render correctly in a screen reader.The Eilenberg Steenrod Axioms and the Locality Principle (PDF)
12 This resource may not render correctly in a screen reader.Subdivision (PDF)
13 This resource may not render correctly in a screen reader.Proof of the Locality Principle (PDF)
II. Computational Methods
14 This resource may not render correctly in a screen reader.CW-Complexes (PDF)
15 This resource may not render correctly in a screen reader.CW-Complexes II (PDF)
16 This resource may not render correctly in a screen reader.Homology of CW-Complexes (PDF)
17 This resource may not render correctly in a screen reader.Real Projective Space (PDF)
18 This resource may not render correctly in a screen reader.Euler Characteristic and Homology Approximation (PDF)
19 This resource may not render correctly in a screen reader.Coefficients (PDF)
20 This resource may not render correctly in a screen reader.Tensor Product (PDF)
21 This resource may not render correctly in a screen reader.Tensor and Tor (PDF)
22 This resource may not render correctly in a screen reader.The Fundamental Theorem of Homological Algebra (PDF)
23 This resource may not render correctly in a screen reader.Hom and Lim (PDF)
24 This resource may not render correctly in a screen reader.Universal Coefficient Theorem (PDF)
25 This resource may not render correctly in a screen reader.Künneth and Eilenberg-Zilber (PDF)
III. Cohomology and Duality
26 This resource may not render correctly in a screen reader.Coproducts, Cohomology (PDF)
27 This resource may not render correctly in a screen reader.Ext and UCT (PDF)
28 This resource may not render correctly in a screen reader.Products in Cohomology (PDF)
29 This resource may not render correctly in a screen reader.Cup Product (cont.) (PDF)
30 This resource may not render correctly in a screen reader.Surfaces and Nondegenerate Symmetric Bilinear Forms (PDF)
31 This resource may not render correctly in a screen reader.Local Coefficients and Orientations (PDF)
32 This resource may not render correctly in a screen reader.Proof of the Orientation Theorem (PDF)
33 This resource may not render correctly in a screen reader.A Plethora of Products (PDF)
34 This resource may not render correctly in a screen reader.Cap Product and “Cech” Cohomology (PDF)
35 This resource may not render correctly in a screen reader.Cech Cohomology as a Cohomology Theory (PDF)
36 This resource may not render correctly in a screen reader.The Fully Relative Cap Product (PDF)
37 This resource may not render correctly in a screen reader.Poincaré Duality (PDF)
38 This resource may not render correctly in a screen reader.Applications (PDF)