$
\newcommand\A{\mathrm{A}}
\newcommand\C{\mathrm{C}}
\newcommand\D{\mathrm{D}}
\newcommand\E{\mathrm{E}}
\newcommand\F{\mathrm{F}}
\newcommand\G{\mathrm{G}}
\newcommand\H{\mathrm{H}}
\newcommand\h{\mathrm{h}}
\newcommand\K{\mathrm{K}}
\newcommand\L{\mathrm{L}}
\newcommand\M{\mathrm{M}}
\newcommand\t{\mathrm{t}}
\newcommand{\bA}{\mathbf{A}}
\newcommand{\bG}{\mathbf{G}}
\newcommand{\bH}{\mathbf{H}}
\newcommand{\bT}{\mathbf{T}}
\newcommand{\bW}{\mathbf{W}}
\newcommand{\Gm}{\bG_m}
\newcommand\Ascr{\mathcal{A}}
\newcommand\Cscr{\mathcal{C}}
\newcommand\Dscr{\mathcal{D}}
\newcommand\Escr{\mathcal{E}}
\newcommand\Kscr{\mathcal{K}}
\newcommand\Lscr{\mathcal{L}}
\newcommand\Oscr{\mathcal{O}}
\newcommand\Perfscr{\mathcal{P}\mathrm{erf}}
\newcommand\Acscr{\mathcal{A}\mathrm{c}}
\newcommand\heart{\heartsuit}
\newcommand\cn{\mathrm{cn}}
\newcommand\op{\mathrm{op}}
\newcommand\gr{\mathrm{gr}}
\newcommand\Gr{\mathrm{Gr}}
\newcommand\fil{\mathrm{fil}}
\newcommand\Ho{\mathrm{Ho}}
\newcommand\dR{\mathrm{dR}}
\newcommand\HH{\mathrm{HH}}
\newcommand\HC{\mathrm{HC}}
\newcommand\HP{\mathrm{HP}}
\newcommand\TC{\mathrm{TC}}
\newcommand\TP{\mathrm{TP}}
\newcommand{\bMap}{\mathbf{Map}}
\newcommand{\End}{\mathrm{End}}
\newcommand{\Mod}{\mathrm{Mod}}
\newcommand{\coMod}{\mathrm{coMod}}
\newcommand{\Fun}{\mathrm{Fun}}
\newcommand{\bMap}{\mathbf{Map}}
\newcommand\bE{\mathbf{E}}
\newcommand\bZ{\mathbf{Z}}
\newcommand\bAM{\mathbf{AM}}
\newcommand\bLM{\mathbf{LM}}
\newcommand\Spec{\mathrm{Spec}}
\newcommand\CAlg{\mathrm{CAlg}}
\newcommand\aCAlg{\mathfrak{a}\CAlg}
\newcommand\dCAlg{\mathfrak{d}\CAlg}
$
Details
Times: MWF 1000.
Place: Lunt Hall 101.
Office hours: MWF 1100 in Lunt Hall 304.
Textbook: Allen Hatcher’s Algebraic Topology, available
on his webpage or at the
campus bookstore.
Catalog description: singular cohomology, the cup product, de Rham cohomology,
sheaf cohomology, Čech cohomology, the Poincaré lemma, the de Rham theorem,
orientability, Poincaré duality, cohomology with compact supports.
Full syllabus: on Canvas.
Syllabus
03/28. The cup product on singular cohomology. The first day of class is Tuesday 03/29.
04/04. Sheaves.
04/11. Sheaf cohomology and Čech cohomology.
04/18. The singular–sheaf cohomology comparison theorem.
04/25. de Rham cohomology.
05/02. The Poincaré lemma and the de Rham theorem.
05/09. Orientability.
05/16. Poincaré duality.
05/23. Cohomology with compact supports.
05/30. No class on Monday to observe Memorial Day. Reading period begins Tuesday; so no class meetings Wednesday or
Friday either.
06/07. Final exam 1500–1700.