Last modified: 23 Jul 2024 10:43
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.
| Study Type | Undergraduate | Level | 4 |
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| Term | Second Term | Credit Points | 15 credits (7.5 ECTS credits) |
| Campus | Aberdeen | Sustained Study | No |
| Co-ordinators |
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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
Information on contact teaching time is available from the course guide.
| Assessment Type | Summative | Weighting | 50 | |
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| Assessment Type | Summative | Weighting | 25 | |
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| Assessment Type | Summative | Weighting | 25 | |
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There are no assessments for this course.
| Assessment Type | Summative | Weighting | ||
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Best of (resit exam mark) or (resit exam mark with carried forward CA marks). |
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| Knowledge Level | Thinking Skill | Outcome |
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| Factual | Understand | Not Available |
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