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Published Nov. 16, 2022 12:50 PM

The oral exams for MAT4540 will be held

  • Tuesday December 13th and
  • Wednesday December 14th.

The exam syllabus consists of

  • Sections 3.1, 3.2, 3.3, 4.1 and 4.2 from Hatcher's "Algebraic Topology".

Each candidate will first be asked to spend 5 to 10 minutes outlining the proof of Theorem 3.15 in the textbook, including as much of the background material needed for this proof as time allows.

Published Nov. 8, 2022 1:02 PM

The oral exam is planned for two days in the week December 12.-16.  Please let me know (at rognes@math.uio.no) if this causes trouble for you.

Published Oct. 3, 2022 12:24 PM

The mandatory assignment is now available.  Submit before 14:30 on Thursday November 3rd using Canvas.

Added Nov. 7, 2022: All submissions have now been graded, and happily approved.

Published Sep. 13, 2022 12:04 PM

Jonas Eidesen (jonaeid@uio.no) is the student representative this semester.

Published Aug. 19, 2022 11:07 AM

Here are my lecture notes from the fall term of 2020.

Published Aug. 16, 2022 6:34 PM

Here is what I wrote to a student asking about the dependence of MAT4540 on MAT4520:

"MAT4540 bygger aldri direkte p? MAT4520, men det er noen paralleller.

I seksjon 3.3 av Hatchers bok "Algebraic Topology" ser vi p? hva som er spesielt med (den singul?re) kohomologien til et rom n?r rommet er en mangfoldighet, s? det er en fordel ? vite hva en mangfoldighet er.  Dette er ogs? nevnt i MAT4500 og MAT4510.  Har man tatt MAT4510 eller MAT4520 har man nok ogs? litt flere eksempler p? flater eller h?yere-dimensjonale mangfoldigheter i tankene enn etter MAT4500.  Det mest kompliserte vi trenger er ? definere hva det vil si at en mangfoldighet er orientert.  Det er flere ekvivalente m?ter ? uttrykke dette, og i MAT4540 vil vi foretrekke en annen m?te enn i MAT4520.  Presentasjonen i MAT4540 vil derfor ikke bygge p? den i MAT4520, men n?r de overlapper kan det v?re intere...

Published Aug. 4, 2022 5:55 PM

The curriculum will be drawn from chapters 3 and 4 of Allen Hatcher's textbook "Algebraic Topology", covering Cohomology and Homotopy Theory.  The transition from homology to cohomology leads to a (cup) product structure that in the case of manifolds satisfies a (Poincaré) duality theorem, represents cohomology classes by maps to (Eilenberg-MacLane) spaces, and leads to a classification of homotopy types by (Postnikov) k-invariants.  We should cover most of sections 3.1, 3.2, 3.3 and large parts of sections 4.1, 4.2 and 4.3.  We may sometimes refer to the results in the appendix on cell complexes.