Caltech Logo

Geometry and Topology Seminar

Friday, October 14, 2022
4:00pm to 5:00pm
Add to Cal
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.