David Hume

David Hume

TDLC Groups

Totally Disconnected Locally Compact Groups, Spring 2018

About the course

Time: Wednesdays 2-4pm, starting January 17th, finishing March 7th.
Credit is obtained by contributing to and/or improving the lecture notes. Suggestions for how to do this are given here.
The course synopsis can be found here.

Previous Lectures

January 17th (Definition of tdlc groups, Van Dantzig's theorem, classification of tdlc groups up to homeomorphism. N.B. The lemma on page 13 should include second countability as an assumption, separability is not sufficient.)
January 24th (Examples: Aut(Γ) continued, direct, semi-direct, restricted and wreath products.)
January 31st (Cayley-Abels graphs, definition and existence for compactly generated groups)
February 7th (Cayley-Abels representations, uniqueness of Cayley-Abels graphs up to quasi-isometry)
February 14th (Locally elliptic groups, Caprace-Monod Minimal Normal Subgroups Theorem)
February 21st (Caprace-Cornulier Non-Embedding Theorem, Topological chief factors)
February 28th (Preliminaries of essentially chief series)
March 7th (Existence and uniqueness of essentially chief series)

Clarifications

Clarifications up to and including Mar 7th Second countability versus separability. More detail in the proof of the Minimal Normal Subgroup Theorem.

References

One of the many different versions of Phillip Wesolek's excellent notes on the subject can be found here.
A very recent survey of important open problems in the area has just been posted by Pierre-Emmanuel Caprace and Nicolas Monod, it can be downloaded from here.