Mike Cummings Research CV

Learning Seminar on Cohomology

Matteus Froese and I want to know: What is cohomology? How do you compute it? What do you do with it? In this seminar, we will aim to answer these questions and more.

Main reference

Schedule

This is our tentative plan; it will be updated as needed. Sections refer to Hatcher.

Date Speaker Topics
September 8 Mike Cummings 2.1 Δ-complexes and simplicial homology
September 15 2.1 Singular homology and homotopy invariance
September 22 2.1 Exact sequences and excision
September 29 2.1 More on excision
October 6 2.1 Equivalence of simplicial and singular homology
October 13 (reading week) 2.2 Degree and cellular homology
October 20 2.2 More on cellular homology
October 27 3.1 Cohomology groups; universal coefficient theorem
November 3 3.1 Cohomology of spaces
November 10 3.2 Cup product
November 17 3.2 More on cup products
November 24 3.3 Orientations and homology, Poincaré duality
December 1 3.3 Connection between duality and the cup product; other forms of duality
December 8 3.F Limits and Ext
December 15 buffer/overflow week