A general Solvable Subgroup Theorem and applications

报告人： Shengkui Ye (New York University-Shanghai)
Time & Date: 16:00 pm, April 3, Thursday
地点： 1510
Zoom Meeting ID: 479 937 5280 (Passcode: SIMIS)
Host: 韩肖垄

摘要： The Solvable Subgroup Theorem says a when a solvable group acting nicely it must be close to an abelian group. It has been proved in many branches of mathematics: Gromoll-Wolf , Lawson-Yau for smooth manifolds, Bridson-Haefliger for CAT(0) spaces, Gersten-Short for biautomatic groups, Conner for stable norms coming from left-invariant metrics, Prytula for systolic complexes, and so on. In this talk, we will discuss a general Solvable Subgroup Theorem, using the notion of length functions on groups. This gives a unified approach to these results. As applications, we will obtain a Solvable Subgroup Theorem for positive topological entropy, solving a problem asked by Hu-Shi-Wang. Furthermore, we will compare the result with the Solvable Subgroup Theorems proved by Haglund for CAT(0) cubical complexes, Dahmani-Fujiwara-Guirardel for Interval Exchange transformations, Minasyan for virtually-cyclic-retract groups, and Koberda for RFRS groups.

About the speaker: Prof. Shengkui Ye is a faculty member at New York University-Shanghai. He obtained his Ph.D. from the National University of Singapore and was a Simons postdoctoral fellow at Oxford University. His research interests lie in geometric group theory and topology.