Abstract: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.
| Comments: | 52 pages, 3 figures. Theorem 1.6 and Section 7 added |
| Subjects: | Geometric Topology (math.GT); Dynamical Systems (math.DS); Group Theory (math.GR) |
| MSC classes: | 20F65, 57S05, 57K20 |
| Cite as: | arXiv:2604.12974 [math.GT] |
| (or arXiv:2604.12974v2 [math.GT] for this version) | |
| https://doi.org/10.48550/arXiv.2604.12974 arXiv-issued DOI via DataCite |
From: Yusen Long [view email]
[v1]
Tue, 14 Apr 2026 17:08:10 UTC (94 KB)
[v2]
Fri, 22 May 2026 16:33:36 UTC (96 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。