Algebraic Topology II (AlgTopII)
This course will be an introduction to homotopy theory and spectral sequences. The first part will focus on elementary homotopy theory covering e.g., fibrations, cofibrations, cellular approximation, Whitehead and Hurewich theorem. The second part will focus on spectral sequences in homotopy theory. The Serre spectral sequence is constructed and used to calculate homology and homotopy groups of a number of interesting spaces.
MSc Programme in Mathematics
- Knowledge: To display knowledge of the course topics and content, at the level of a beginning researcher.
- Skills: To be able to use the acquired knowledge to perform computations.
- Competencies: To be able to produce independent proofs in extension of the acquired knowledge.
4 hours lectures and 3 hours exercises per week for 9 weeks.
In previous years we have roughly followed Chapter 4 (Homotopy Theory) and Chapter 5 (Spectral Sequences) of Hatcher's book "Algebraic Topology". (This book is available from his website and bookstores.)
Algebraic Topology (AlgTop) and Homological Algebra (HomAlg), or
equivalent. Algebraic Topology 1.5 (AlgTop 1.5) can also be
advantageous. (These courses cover more or less the equivalent of
the first 3 chapters of Hatcher's book Algebraic Topology.)
Academic qualifications equivalent to a BSc degree is recommended.
- 7,5 ECTS
- Type of assessment
Continuous assessmentWeekly homework counting 50 % towards the grade and a 2 hours 'closed-book' final in-class problem set counting 50 % of the grade.
- Only certain aids allowed
All aids allowed for the weekly homework. No books and no electronic aids are allowed for the 2 hours final exam. Personally created handwritten notes on paper are allowed.
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner.
Criteria for exam assessment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Single subject courses (day)
- Theory exercises
- Course number
- 7,5 ECTS
- Programme level
- Full Degree Master
- No limit
- Study Board of Mathematics and Computer Science
- Department of Mathematical Sciences
- Faculty of Science
- Jesper Grodal (2-79764f7c7083773d7a843d737a)
- Piotr Pstragowski (5-746d737876447165786c326f7932686f)
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