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MX4546: ALGEBRAIC TOPOLOGY (2020-2021)

Last modified: 05 Aug 2021 13:04


Course Overview

Algebraic topology is a tool for solving topological or geometric problems with the use of algebra. Typically, a difficult geometric or topological problem is translated into a problem in commutative algebra or group theory. Solutions to the algebraic problem then provide us with a partial solution to the original topological one.





Course Details

Study Type Undergraduate Level 4
Session Second Sub Session Credit Points 15 credits (7.5 ECTS credits)
Campus Aberdeen Sustained Study No
Co-ordinators
  • School Administrativ Julie Timms

Qualification Prerequisites

  • Programme Level 4

What courses & programmes must have been taken before this course?

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

No

Course Description

Elementary concepts of homotopy theory.

The fundamental group and its naturality properties.

Fundamental groups and covering spaces.

Free groups and amalgamated products

The Seifert-Van Kampen theorem

Presentations of groups.

 

Syllabus:

 

Revision of topological spaces

Topological equivalence, homotopy and homotopy equivalence, deformation retraction.

The fundamental group, homomorphisms induced by continuous maps, and homotopy invariance.

The fundamental group of a circle and introduction to covering spaces

Applications: The fundamental theorem of algebra, Brauer fixed point, and Borsuk-Ulam.

Covering spaces: Concept, existence and classification.

Desk transformation and group actions.

The Seifert Van-Kampen theorem.

Computation of the fundamental group


In light of Covid-19 this information is indicative and may be subject to change.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

  • 1 during University weeks 25 - 29, 31 - 34, 38 - 39
  • 1 Tutorial during University weeks 26 - 29, 31 - 34, 38 - 39

More Information about Week Numbers


In light of Covid-19 and the move to blended learning delivery the assessment information advertised for second half-session courses may be subject to change. All updates for second-half session courses will be actioned in advance of the second half-session teaching starting. Please check back regularly for updates.

Summative Assessments

2 x standard course assessments - 30% each

One seminar/essay - 40%

Alternative Resit Arrangements for students taking course in Academic Year 2020/21

Resubmission of failed elements (pass marks carried forward)

Formative Assessment

There are no assessments for this course.

Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
FactualUnderstandNot Available

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