Faculty of Science

Algebraic Topology II (AlgTopII)
Provider: Faculty of Science

Activity no.: 5598-23-07-31
	Enrollment deadline: 24/04/2023

Place

Department of Mathematical Sciences

Date and time

24.04.2023, at: 08:00 - 23.06.2023, at: 16:00

Regular seats

ECTS credits

7.50

Contact person

Nina Weisse E-mail address: weisse@math.ku.dk

Enrolment Handling/Course Organiser

Jesper Grodal E-mail address: jg@math.ku.dk

Written language

English

Teaching language

English

Semester/Block

Block 4

Scheme group

Exam form

Continuous assessment

Exam form

Continuous assessment

Exam details

Weekly 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 scale

7 point grading scale. For PhD students: Passed / Not Passed

Course workload

Course workload category	Hours
Preparation	134.00
Lectures	36.00
Theory exercises	36.00

Sum	206.00

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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