Last modified: 05 Aug 2021 13:04
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.
|Session||Second Sub Session||Credit Points||15 credits (7.5 ECTS credits)|
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.
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
Information on contact teaching time is available from the course guide.
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)
There are no assessments for this course.
|Knowledge Level||Thinking Skill||Outcome|