South African - Japanese Discrete Homotopy Meeting 2025 (Cape Town, South Africa, 10-11 September 2025)

10th of September 2025  - 15.00/16.00  and 11th of September 2025  - 14.00/16.00  

Venue: MAM111 - Department of Mathematics and Applied Mathematics - University of Cape Town

Speaker:   Yanga Bavuma (University of Cape Town, Cape Town, South Africa)

Title:          Short course in basic algebraic topology 

Abstract:  By using the ideas documenting holes in spaces, we can characterise properties of a space via algebraic objects, i.e. groups. I will be giving introductory talks to both homotopy groups and (simplicial) homology groups and highlight the differences in these two approaches to motivate the proposed project of the conference. 

I will assume a limited knowledge of topology from the audience. And give geometrically flavoured descriptions of the groups. The approach of homotopy groups will be given from the perspective of the book, 

C. Kosniowski, A First Course in Algebraic Topology (Cambridge University Press, 1980, Cambridge),

where I will cover the motivation for the groups and their generalisations. The approach of (simplicial) homology groups will be given from the perspective of the book, 

A. Hatcher, Algebraic Topology (Cambridge University Press, 2002, Cambridge), 

where I will cover the motivation for the groups and their generalisations.