3 papers
math.GR2025
The Ribes-ZalesskiÄ product theorem via foldings and extensions
Zhaoshen Zhai
We present an exposition of the Auinger-Steinberg proof of the Ribes-ZalesskiÄ product theorem for pro-V topologies, where V is a pseudovariety of groups closed under extensions w…
math.GT2025
A saturated 1-system of curves on the surface of genus 3
Zhaoshen Zhai
We construct a system of 33 essential simple closed curves that are pairwise non-homotopic and intersect at most once on the oriented, closed surface of genus 3. Moreover, we show…
math.LO2025
Quasi-treeings are treeable: a streamlined proof
Zhaoshen Zhai
We present a streamlined exposition of a construction by R. Chen, A. Poulin, R. Tao, and A. Tserunyan, which proves the treeability of equivalence relations generated by any locall…