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Junior Topology
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Lvzhou (Joe) Chen, Zoom: The Kervaire conjecture and the minimal complexity of surfaces
Wednesday, September 15, 2021, 02:00pm - 03:00pm
Abstract: We use topological methods to solve special cases of a fundamental problem in group theory, the Kervaire conjecture. The conjecture asserts that, for any nontrivial group G and any element w in the free product G*Z, the quotient (G*Z)/w is still nontrivial. We interpret this as a problem of estimating the minimal complexity (in terms of Euler characteristic) of surfaces in HNN extensions. This gives a conceptually simple proof of Klyachko's theorem that confirms the Kervaire conjecture for any G torsion-free. I will also explain new results obtained using this approach.
Location: Zoom

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