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Algebraic Topology II (AlgTopII)
Provider: Faculty of Science

Activity no.: 5598-23-07-31 
Enrollment deadline: 24/04/2023
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time24.04.2023, at: 08:00 - 23.06.2023, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserJesper Grodal    E-mail address: jg@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 4
Scheme groupB
Exam formContinuous assessment
Exam formContinuous assessment
Exam detailsWeekly homework (each weighted equally, accounting for 70% of the grade) and a final in-class problem set (accounting for 30% of the grade). You will have three hours for the in-class problem set.
Grading scale7 point grading scale. For PhD students: Passed / Not Passed
Course workload
Course workload categoryHours
Preparation134.00
Lectures36.00
Theory exercises36.00
Sum206.00
Content
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.

Learning outcome
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.

Literature
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.)

Target group

Teaching and learning methods
4 hours lectures and 4 hours exercises per week for 9 weeks.

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