This is the second weekend in a row spent to more or less large part in the office, working with the product structures on cohomology. Reason for this is that I’m getting my share of the department seminars now – I’m to walk us through the Yoneda cohomology product; the cohomology-as-Hom-in-a-derived-category viewpoint; their equivalence to one another as well as to the cup product; and then talk about restriction and corestriction (i.e. what happens to cohomology when we go between kG- and kH-modules for H a subgroup of G)
This is all not really very bad – I really, really, REALLY need to get a solid grip of this myself too. Only; when I started working on it, I thought I had 4 days and not 11 to prepare in – and dove right into it. Maybe a bit too deeply, so when I (monday) found out I didn’t need to get it done THAT quickly, I kinda dropped most of it for the rest of the week. And now, I need to find a decent proof that cup products = Yoneda products. And I just realized that my books don’t really cover it.
In other news, the apartment I looked at last week now is mine. The lease is signed. My stuff is in it (though not really where it should be – I have a week or two of unpacking to do!!) and I spent a major part of today running around Jena, getting hold of essentials – such as a duvet cover (I didn’t discover the lack of it until I went to bed yesterday) and looking at a new bed (the one that’s there already is MURDER on my back!).
I also need to get hold of a rather highpowered WLAN card and an external directional antenna. My boss’s laptop has good reception, my USB stick with a homebuilt cantenna around it has lousy reception, and the stick on its own has no reception right now. Anyone have any experience with such things? I’d love advice!