MATH 7221 — Topology 2
4 semester hoursGraduateLectureusually offered: falltypical days: M/W/ThBostonTraditional
Continues MATH 5121. Introduces homology and cohomology theory. Studies singular homology, homological algebra (exact sequences, axioms), Mayer-Vietoris sequence, CW-complexes and cellular homology, calculation of homology of cellular spaces, and homology with coefficients. Moves on to cohomology theory, universal coefficients theorems, Bockstein homomorphism, Künneth formula, cup and cap products, Hopf invariant, Borsuk-Ulam theorem, and Brouwer and Lefschetz-Hopf fixed-point theorems. Ends with a study of duality in manifolds including orientation bundle, Poincaré duality, Lefschetz duality, Alexander duality, Euler class, Lefschetz numbers, Gysin sequence, intersection form, and signature.
Offering history
| Term | Sections | Enrolled | Capacity | Full | Open seats/section |
|---|---|---|---|---|---|
| Fall 2023 | 1 | 14 | 20 | 70% | 6.0 |
| Fall 2024 | 1 | 9 | 20 | 45% | 11.0 |
Snapshots from scheduled scrapes — not live seat availability. "Full" can exceed 100% when sections over-enroll.
Meeting times
Share of recent sections by weekday: M 100% · T 0% · W 100% · Th 61% · F 0%
Common patterns: MWR (61% of sections), MW (39% of sections) — in patterns, R means Thursday
Professors
Fall
- Benjamin Knudsen (100% of students) · reviews
Percentages are each professor's average share of the season's enrolled students in recent terms.
Unlocks
Courses that list MATH 7221 in their prerequisites.
Links
Official catalog (MATH course descriptions) · Student reviews on RateMyHusky · All MATH courses · Plan it at numap.app