arXiv subjects

Rodrigo De Pool

Publications and source records attributed to Rodrigo De Pool.

3 recordsLinked to original sources

arXiv2026

Rigidity of maps between configuration spaces

Let $n\geq5$ and $m\geq3$. Let $\Phi\colon\mathrm{B}_n\to\mathrm{B}_m$ be a homomorphism of braid groups. We prove that if the image of $\Phi$ is irreducible and not cyclic, then $m=n$ and $\Phi$ agrees with an automorphism modulo the center $Z(\mathrm{B}_m)$. This resolves in the affirmative a conjecture of Chen, Kordek, and Margalit. It also provides a partial resolution to a problem on the K3 problem list. As a consequence, we prove that every holomorphic map $\mathrm{UConf}_n(\mathbb{C})\to\mathrm{UConf}_m(\mathbb{C})$ for $n\geq5$ and $m\geq3$ is affine equivalent to either a constant map or the identity map. This resolves a conjecture of Farb for $n\neq4$.

math.GT↗

arXiv2024

Holomorphic maps between moduli spaces II

We prove that forgetful maps are the only non-constant holomorphic maps $\mathcal{M}_{g,r}\to \mathcal{M}_{g',r'}$ between moduli spaces, as long as $g\ge 4$ and $g'\le 3\cdot 2^{g-3}$.

math.GT↗

arXiv2024

Non-planar ends are continuously unforgettable

We show that continuous epimorphisms between a class of subgroups of mapping class groups of orientable infinite-genus 2-manifolds with no planar ends are always induced by homeomorphisms. This class of subgroups includes the pure mapping class group, the closure of the compactly supported mapping classes, and the full mapping class group in the case that the underlying manifold has a finite number of ends or is perfectly self-similar. As a corollary, these groups are Hopfian topological groups.

math.GT↗