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Geometry and Topology Seminar

Friday, October 14, 2022
4:00pm to 5:00pm
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Linde Hall 187
The Kervaire conjecture and the minimal complexity of surfaces
Lvzhou Chen, Department of Mathematics, Purdue University,

We use topological methods to solve special cases of a fundamental problem in group theory, the Kervaire conjecture, which has connection to various problems in topology. 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 surface maps to certain spaces. This gives a conceptually simple proof of Klyachko's theorem that confirms the Kervaire conjecture for any G torsion-free. We also obtain new results concerning injectivity of the map G->(G*Z)/<<w>> when w is a proper power.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected] or visit https://sites.google.com/site/caltechgtseminar/home.