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Categories and Topology (CatTop)
Provider: Faculty of Science

Activity no.: 5550-21-07-31 
Enrollment deadline: 06/09/2021
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time06.09.2021, at: 08:00 - 12.11.2021, 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 1
Scheme groupB
Exam requirementsThe student must in a satisfactory way demonstrate that he/she has mastered the learning outcome
Exam formContinuous assessment
Exam detailsWeekly exercises
Grading scalePassed / Not passed
Censorship formOne internal examiner
Exam re-examination30 minutes oral exam without preparation time. No aids allowed. Several internal examiners
Course workload
Course workload categoryHours
Lectures36.00
Theory exercises36.00
Preparation134.00
Sum206.00
Content
Topics in algebraic topology centered around the use of categories in homotopy theory and simplicial methods. Topics include simplicial sets, nerves of categories, classifying spaces, homotopy (co)limits, localization and completion.

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 lecture notes were used. It will be aimed to make these notes available from Absalon and/or the lecturers homepage.

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

Remarks
Academic qualifications:

Knowledge of foundational algebraic topology corresponding to roughly Chapter 1-5 in Hatcher's book "Algebraic Topology" is assumed (e.g., obtained thorough the UCPH courses AlgTop, HomAlg and AlgTopII).

Academic qualifications equivalent to a BSc degree is recommended.

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