My first week has passed. Today is saturday; and the move took place monday. So far, I’ve been running around doing bureaucracy and little else (I managed to leaf through the first 5 pages of Evens: Cohomology of Groups). Along the lines – I’ve received a summons to appear in front of the immigration authorities to explain my moving in, I’ve ran circles around the city trying to get someone to approve my swedish birth certificate et.c.
My apartment is small, neat and nice. It’s some 4×5 meters, with bed, bookcase, two tables, wardrobe, kitchenette, toilet with bath, balcony. And then all the things I brought with me – including a bookcase, three tables, computer, books-books-books, and much much more. I’ve gotten around to some interior decoration as well – putting up my swedish and my franconian flags on a wall. The endeffect is pretty – although I periodically have to remind myself that my putting up a swedish flag is no longer a sign of right-extremism but rather a sign of keeping in touch with home.
Mathematically, I’m slowly getting to grips with the concept of the cohomology of a group. Basically, I’m back to studying Ext_R(k,k) for a specific k-algebra R – which in this case happens to be the group ring kG. As such, it’s more or less the same generic area as during my master’s thesis. I am more and more warming up to the idea of involving as much homotopy theory as possible; I know that finding contracting homotopies (i.e. a chain homotopy between the chain maps 0 and Id on a given chain complex) makes verification of resolutions simple; and if Morse theory can be involved to condense the complexes to something of manageable size, then the computational barriers we’re facing’d be more easily treated as well. In end-effect, this all boils down to me wanting to learn more about algebraic homotopy theory / homotopical algebra; and I’ll probably start by studying model categories from Quillen, Dwyer & Spalinski and from Hovey.
At some point in the future, I will get my internet access @home up and running. And then woe upon the mean ugly hordies, I say!