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.
Pre-requisites: MATH2003 AND MATH2049 OR MATH3079