$ \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: On Zoom (first two weeks) and then in Lunt Hall 101.

Office hours: MWF 1100 on Zoom (first two weeks) and then in Lunt Hall 304.

Textbook: Course notes distributed on Canvas and Allen Hatcher’s Algebraic Topology, available on his webpage or at the campus bookstore.

Catalog description: the fundamental group of a space, covering spaces, and the van Kampen theorem; singular homology, Mayer–Vietoris, degree, and Euler characteristics.

Full syllabus: on Canvas.

Syllabus

01/03. Homotopy groups.

01/10. Covering spaces.

01/17. Universal covers. No class on Monday to observe MLK day.

01/24. The van Kampen theorem.

01/31. Examples.

02/07. Singular homology.

02/14. Homological algebra.

02/21. Excision and Mayer–Vietoris.

02/28. Degree and CW homology.

03/07. Wrap-up. Reading period begins Tuesday; no class meetings Wednesday or Friday, so Monday is the last day of the course.

03/17. Final exam 1500–1700 if necessary.