Nov 11, Nov 18 & Nov 25: Em & Ryan on Sheaf cohomology [worksheet day 1]
Suggested Reading: Chapter 2, page no: 71-92 in Ravi Vakil textbook: The Rising Sea.
Dec 2 & Dec 9: Isaiah & Kesavan on Čech cohomology.
Oct 28 & Nov 4: Nick & Stephen on de Rham cohomology [worksheet day 1] [worksheet day 2]
Suggested Reading: Chapter 1, page no: 13-19 in Bott-Tu textbook: Differential Forms in Algebraic Topology.
Oct 14: Catch up day!
No reading. Instead, we'll have time to go back and do exercises on past worksheets.
Oct 7: Yuhan & Pablo on Poincare duality [worksheet]
Suggested Reading: Hatcher page 230 - 233, 239-242, 245 – 249.
Alternatively, see Munkres section 63 (just intro+ Thm63.2 + Cor63.3), section 65 & section 67.
Sep 30: Sam & Yavuz on cup & cap product [worksheet]
Suggested Reading: Hatcher subsections Cup product (pg 206-212), Cap product (pg 239-242), and Connections between Cup & Cap product (pg 249).
Alternatively, sections 48 and 66 of Munkres.
Sep 23: Kesavan & Ryan on The universal coefficient theorem and compact support [worksheet]
Suggested reading: Hatcher Cohomology with Compact Supports (pgs 242-245), Universal Coefficients for cohomology (pgs 190-197).
Alternatively, Munkres Sections 53&55, and possibly Section 58&60.
Sep 16: Lukas & Mikkel on Eilenberg-Steenrod axioms for cohomology [worksheet] [solutions]
Suggested Reading: Hatcher section 2.3 (or alternatively, Munkres section 26).
Sep 9: Pablo & Julia on singular cohomology & Mayer-Vietoris [worksheet]
Suggested reading: HAT subsections "Singular Homology" (In Section 2.1, pgs 108-110), and perhaps "Mayer-Vietoris Sequences" (In Section 2.2, pgs 149-153 for homology; at the very end of Section 3.1, pgs 203-204 for cohomology).
Alternate reading option covering ~ the same content: MAT Sec. 29 + Sec. 33
Sep 2: Isaiah & Anna on simplicial + CW cohomology, continued. [worksheet] [solutions]
Suggested reading: HAT subsections "Idea of Cohomology" (intro to Ch 3, pg 186-189) + "Cellular Homology" from Lemma 2.34 - Ex 2.42 (mid section 2.2, pg 137-144) + "Simplicial Cohomology" & "Cellular Cohomology" (end of 3.1, pg 202-203).
Alternate reading option covering ~ the same content: MAT Thm 42.1 + Sec. 38 + Sec. 47.
Aug 26: Anna on simplicial + CW cohomology; and organizational discussion. (No reading, no worksheet)