Seminar| Institute of Mathematical Sciences
Time: Wednesday, Apirl 22th, 2026,16:00-17:00
Location: IMS, RS408
Speaker: Ze Zhou, Shenzhen University
Abstract: We show that a $d$-dimensional smooth manifold $M$ is diffeomorphic to $\mathbb R^d$ if it admits a Lyapunov-Reeb function, i.e., a smooth map $f:M\to \mathbb R$ that is proper, lower-bounded, and has a unique critical point. By constructing such functions, we prove that the moduli spaces of self-avoiding polygonal linkages and configurations are diffeomorphic to Euclidean spaces. This resolves the Refined Carpenter's Rule Problem and confirms a conjecture posed by Gonzalez and Sedano-Mendoza. Furthermore, we describe foliation structures of these moduli spaces via level sets of Lyapunov-Reeb functions and develop algorithms for related problems. This is a joint work with Te Ba.