Mr. Danny Gillam will give the talk on Friday, April 16 at noon in Math 417. This lecture will be open to graduate and undergraduate students only.
Abstract: Can the additive group of rationals arise as the fundamental group of a "reasonable" topological space? It will be shown that the answer is "no" if "reasonable" is construed to mean "compact, metric, path connected, and locally path connected". The intention is to prove Shelah's result that such a space has a fundamental group which is either finitely-generated or has the cardinality of the continuum. Some basic intuitive notion of fundamental group is assumed, but the methods used are essentially elementary. It is necessary to make use of a lemma from set-theoretic model theory concerning analytic equivalence relations, which is established by a forcing argument. This will be sketched as time permits, but the intention is to keep the talk otherwise self-contained.
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