Last week Matthias Wendt and I have put our first joint paper on the arXiv, it's called "A¹-fundamental groups of isotropic reductive groups" and here I will tell you how you can think about it without going through all definitions.

I have blogged about this before, but until a few days ago, there was only my diploma thesis in german and an extended abstract in english online, and the results were not as general (oh, and the proofs were also not the best...).

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Now this is a slightly corrected (although still somewhat messy) version of my diploma thesis - in german:
Matsumotos Satz und A¹-Homotopietheorie.

You can read something about the content in this blog post, containing an extended abstract in english.

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Nearly half of all blog posts start with "Soon this blog will be full of content" and the other half with "it has been incredibly silent, soon I will post a lot". This post is of the second type, but I apologize by linking to what has kept me from writing here:
Extended abstract of my diploma thesis.
While the diploma thesis is in german, the abstract is in english and only 9 pages long, without any proofs. The diploma thesis is now available here (updated on 2011-08-09).

As a teaser, here is the abstract of the abstract:

In classical covering space theory we have an isomorphism of the fundamental group with the fibre of the universal cover over the basepoint. Covering spaces of topological groups are group extensions, but not every group extension is a covering space. Perfect groups admit a universal central extension and the kernel of this extension is also called fundamental group. For simply connected Chevalley-groups over a perfect field, this fundamental group, classically called second unstable K-Theory, is exactly the fundamental group of a simplicial resolution. The loops are described explicitly by matrices.

Today I'm attending the second Workshop on Personal Knowledge Management (PKM2010) at the Human-Computer-Interaction (HCI) conference "Mensch und Computer" in Duisburg (Germany).

I have absolutely no idea what to expect, so I expect to be surprised.

UPDATE: Now that the workshop is almost over (coffee break right now), maybe the most important for me:

It was fun!

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