Homogeneity of the free group
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Tue, 08/03/2011 17:00 |
Dr Chloé Perin (Strasbourg) |
Algebra Seminar  |
L2 |
| Following the works of Sela and Kharlampovich-Myasnikov on the Tarski problem, we are interested in the first-order logic of free (and more generally hyperbolic) groups. It turns out that techniques from geometric group theory can be used to answer many questions coming from model theory on these groups. We showed with Sklinos that free groups of finite rank are homogeneous, namely that two tuples of elements which have the same first-order properties are in the same orbit under the action of the automorphism group. We also show that this is not the case for most surface groups. | |||