Ghana Prepreplanning
August-24-09
8:35 AM
Margaret (and Isaac),
Ok, I thought some more and here's my proposal.
My overall title in Legon will be "Homology". I will be talking for three
hours a day, (say) two in the morning and one in the early afternoon, with
the understanding that the afternoon class may sometimes extend a bit more
than an hour if we need to finish a subject. To the extent there is
interest I will stay around and be available for students until later in
the afternoon or evening. This will go on for two weeks of five days per
week.
On the first week I will talk about singular homology of topological
spaces with the goal of saying everything that is necessary to prove the
Brouwer fixed point theorem by computing the homology groups of spheres
using excision, short and long exact sequences, homotopy invariance, etc.
Everything that I will say is in many books and is at least 50 years old.
On the second week I will move on to talk about Khovanov homology for
knots. This will be a quick introduction to a very hot topic of current
research in knot theory, and while I will make no direct use of the
results of the first week, many of the concepts introduced in the first
week will have to be used again and extended in the second. So the overall
theme will remain the same, and thus the overall title will be "homology".
The second week will be a little less dense than the first, so the first
may overflow a bit into the second. We will not make plans for talks on
any of the "isolated" topics I proposed earlier, yet if there is interest
and energy left, we may add such talks as appropriate.
I will then travel by land to Kumasi and spend Monday and Tuesday June 28
and 29 there, and give one or two talks on isolated topics in coordination
with Isaac Dontwi. On June 30 I will return to Toronto.
My internal notes on the subject are at
[link]
and especially at
[link].
These pages will continue to evolve later on.
Let me know what you think; I'll be happy to hold another phone meeting
soon to see what changes need to be made...
Best,
Dror.