Courses / Modules / MATH6137 Homotopy and Homology

Homotopy and Homology

When you'll study it: Semester 2
CATS points: 15
ECTS points: 7.5
Level: Level 7
Module lead: Ruben Sanchez Garcia
Academic year: 2025-26

Module overview

Homotopy theory is the study of continuous deformations. A geometric object may be continuously deformed by pulling, stretching, pressing or compressing, but not by tearing or puncturing (which are discontinuous). Two objects can then be regarded as equivalent if one can be continuously deformed into the other and vice-versa. The goal of homotopy theory is to determine which geometric objects are equivalent in this sense, or not. To do this, methods are needed which assign algebraic information to these geometric objects which are invariant (stay the same) under continuous deformations. Examples consider in the module are homotopy groups and homology groups.

Linked modules

Pre-requisites: MATH2003 AND MATH2049 OR MATH3079

Learning and Teaching

Teaching and learning methods

Lectures and weekly problem sheets. Private study is also important for work on the problem sheets.

Study time
Type	Hours
Independent Study	114
Teaching	36
Total study time	150

Resources & Reading list

Textbooks

Allen Hatcher (2001). Algebraic Topology. Cambridge: Cambridge University Press.

Assessment

Summative

This is how we’ll formally assess what you have learned in this module.

Breakdown
Method	Percentage contribution
Coursework	100%

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Breakdown
Method	Percentage contribution
Exam	100%

Repeat Information

Repeat type: Internal & External