6 papers
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…
An explicit exotic representation of a rank-one simple Lie group via convex bodies
François Fillastre, Yusen Long, David Xu
In [DP12], Delzant and Py showed that there exist continuous irreducible isometric actions of on the infinite-dimensional hyperbolic space $\mathbb{H}^…
Non-amenability of mapping class groups of infinite-type surfaces and graphs
Yusen Long
This paper completely determines the non-amenability of the mapping class groups of infinite-type surfaces, the mapping class groups of locally finite infinite graphs of higher ran…
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…
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…
Hyperbolic embedding of infinite-dimensional convex bodies
Yusen Long
In this article, we use the second intrinsic volume to define a metric on the space of homothetic classes of Gaussian bounded convex bodies in a separable real Hilbert space. Using…