I added a section about amenability (5.8), corrected many misprints. Here is the latest version of the book. Advertisements

Most probably I won’t be active on mathoverflow.net any longer: too many homework level questions and the community attitude towards these questions has become too liberal. I think I did help a few people with my answers, and I got some useful information from the answers to my questions.

Here is an adaptation of Lang’s proof of Gelfond’s theorem to prove that is not rational – needed for http://mathoverflow.net/questions/138247/prove-that-sqrt2-sqrt2-is-an-irrational-number-without-using-a-theorem/138291#138291. Consider the functions . Let , where is big enough (we shall see how large should be below). Suppose that is rational. Then is a rational number for every . Lemma 1. Let us have […]

Here are a few problems that I think are nice. Find a finitely presented group with uncountably many non-homeomorphic (or even non -equivalent) asymptotic cones, independent of Continuum Hypothesis. Recall that if we assume that CH is false than any uniform lattice in is an example (see Kramer, Shelah, Tent, Thomas, http://front.math.ucdavis.edu/0306.5420). The maximal number […]

Here are some of the strangest points in the Grovers’s boycott letter. 1. Elsevier sells journals to libraries in “bundles” which Gowers does not like because his library has to pay both for the journals he wants and for the journals he does not fancy. What makes this objection strange is that “bundling” is a […]

One of the features of my book, “Non-commutative combinatorial algebra” is a road map of Olshanskii’s proof of the celebrated Novikov-Adian’s theorem: for every large enough odd there exists a finitely generated infinite group of exponent $n$. The goal was to present the main ideas and the main methods of the proof without getting too […]

More about editorial business. Here is why I think Gowers’s boycott of Elsevier is “ill-advised”. The real effect of the boycott is that when an editor of an Elsevier journal (J. of Algebra, JPAA, etc.) sends a referee request to some specialist, the specialist refuses to referee because he/she does not like Elsevier. This does […]