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MX5506: ALGEBRAIC TOPOLOGY (2014-2015)

Last modified: 28 Jun 2018 10:27


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 Postgraduate Level 5
Session Second Sub Session Credit Points 20 credits (10 ECTS credits)
Campus None. Sustained Study No
Co-ordinators
  • Dr Diarmuid Crowley

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

None.

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 natural properties. Fundamental groups and covering spaces. Free groups and subgroups of free groups. The Seifert-van Kampen theorem. Presentations of groups. The concept of a surface. Triangulations. The classification of Compact surfaces without boundary. If time allow, an introduction to homology theory.

Contact Teaching Time

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

Teaching Breakdown

More Information about Week Numbers


Details, including assessments, may be subject to change until 31 August 2023 for 1st half-session courses and 22 December 2023 for 2nd half-session courses.

Summative Assessments

One 3-hour written examination (80%); one in-course assessment (20%).

Formative Assessment

There are no assessments for this course.

Feedback

None.

Course Learning Outcomes

None.

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