Ehresmann, Koszul and Cartan connections on fibre bundles

This is the website for a mini-course on connections on fibre bundles to be delivered by José Figueroa-O'Farrill. There are six 2-hour lectures planned, but we may add the odd additional lecture if we run out of time.

It is often stated that Differential Geometry is the study of connections on fibre bundles. At the same time, it is hard to overestimate how appropriate this language is in the mathematical description of the physical world: be it the rôle it continues to play in gauge theory and (super)gravity or the rôle it is expected to play beyond Lorentzian geometry. The aim of these lectures is to introduce the language and see some examples of Ehresmann connections on principal fibre bundles, Koszul connections on vector bundles and Cartan connections on fibre bundles associated to Klein geometries.

Schedule of seminars

  1. Friday, 8 November 2019, 2-4pm
    JCMB 4325B
  2. Tuesday, 12 November 2019, 2-4pm
    JCMB 5323
  3. Wednesday, 20 November 2019, 4-6pm
    JCMB 4312
  4. Friday, 29 November 2019, 2-4pm
    JCMB 4325B
  5. Friday, 6 December 2019, 2-4pm
    JCMB 5323
  6. Friday, 13 December 2019, 2-4pm
    JCMB 5323


The links below are to the hand-written notes as well to some sources I found useful. Thanks to Linden Disney-Hogg, we now have typeset notes. There is a google form for comments (e.g., found typos) on the notes.

j.m.figueroa at
Last modified: Wed Oct 9 11:15:40 BST 2019