Tuesdays 2-3pm; location AVH 351.
This is a reading group on cohomology which will build off of the material in Topology II. We will use Allen Hatcher's Algebraic Topology book as our reference. Each week, everyone will read a bit about the material, but one or two students will be in charge of leading the discussion, perhaps by giving a short recap and curating some exercises.
Tentative topics include:
Simplicial/CW cohomology
Singular cohomology
Cup and cap products
Poincaré duality
Čech cohomology
De Rham cohomology
Sheaf cohomology
The prerequisite material for this is Math 872, though when we get to sheaf cohomology, Math 915 will probably be a useful corequisite.
Hatcher's Algebraic Topology = HAT is the main source. HAT page numbers are from the edition located at this link.
Munkres's Algebraic Topology = MAT is another nice algebraic topology textbook. Some weeks we might provide alternative reading suggestions from MAT. You are not meant to do both, but some of you who have a copy of MAT might prefer it to HAT.
For more info, contact Jack Jeffries, Anna Brosowsky, or Kesavan Mohana Sundaram.