arXiv subjects

Yongsheng Jia

Publications and source records attributed to Yongsheng Jia.

2 recordsLinked to original sources

arXiv2026

Fine projection complex and subsurface homeomorphisms with positive stable commutator length

Drawing inspiration from [BBF15], we construct a family of unbounded quasi-trees for a connected closed oriented surface $S_g$ of genus $g\geq 2$, upon which the group $\mathrm{Homeo}_0(S_g)$ acts coboundedly by isometries. As an application, we show that some surface homeomorphisms preserving a non-sporadic essential subsurface or an essential subsurface homeomorphic to a once-bordered torus can have positive stable commutator length in $\mathrm{Homeo}_0(S_g)$. Moreover, we provide a version of projection complex that does not require the finiteness condition.

math.GT↗

arXiv2025

Balanced curves, quasimorphisms, and the equator conjecture

We construct a new infinite-dimensional family of homogeneous quasimorphisms on the group of Hamiltonian diffeomorphisms of the two-sphere. Moreover, for any constant $K$ less than the total area of the sphere, we produce unbounded homogeneous quasimorphisms that vanish on any map supported on some disk of area at most $K$. As an application, we prove an analogue of the equator conjecture, namely that the space of equators equipped with any choice of quantitative fragmentation metric has infinite diameter. To prove our results, we introduce tools that draw inspiration from the theory of curve graphs used to study mapping class groups.

math.SG↗