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math.GT2026
Fine projection complex and subsurface homeomorphisms with positive stable commutator length
Yongsheng Jia, Yusen Long
Drawing inspiration from [BBF15], we construct a family of unbounded quasi-trees for a connected closed oriented surface of genus , upon which the group $\mathrm{Hom…
math.GT2024
Connectedness of the Gromov boundary of fine curve graphs
Yusen Long, Dong Tan
The fine curve graph was introduced to study homeomorphism group of surfaces. In this paper we study the topology of the Gromov boundary of this graph for closed surfaces with high…
math.GT2023
Big mapping class groups are not extremely amenable
Yusen Long
This paper uses the renowned Kechris-Pestov-Todorčević machinery to show that (big) mapping class groups are not extremely amenable unless the underlying surface is a sphere or a o…