Fine projection complex and subsurface homeomorphisms with positive stable commutator length
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913156219011072 |
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| author | Jia, Yongsheng Long, Yusen |
| author_facet | Jia, Yongsheng Long, Yusen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12974 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fine projection complex and subsurface homeomorphisms with positive stable commutator length Jia, Yongsheng Long, Yusen Geometric Topology Dynamical Systems Group Theory 20F65, 57S05, 57K20 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. |
| title | Fine projection complex and subsurface homeomorphisms with positive stable commutator length |
| topic | Geometric Topology Dynamical Systems Group Theory 20F65, 57S05, 57K20 |
| url | https://arxiv.org/abs/2604.12974 |