Bavard duality for the relative Gromov seminorm
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909287173849088 |
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| author | Marchand, Alexis |
| author_facet | Marchand, Alexis |
| contents | The relative Gromov seminorm is a finer invariant than stable commutator length where a relative homology class is fixed. We show a duality result between bounded cohomology and the relative Gromov seminorm, analogously to Bavard duality for scl. We give an application to computations of scl in graphs of groups. We also explain how our duality result can be given a purely algebraic interpretation via a relative version of the Hopf formula. Moreover, we show that this leads to a natural generalisation of a result of Calegari on a connection between scl and the rotation quasimorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_02149 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bavard duality for the relative Gromov seminorm Marchand, Alexis Geometric Topology Group Theory 20J05, 57M07, 55M05 The relative Gromov seminorm is a finer invariant than stable commutator length where a relative homology class is fixed. We show a duality result between bounded cohomology and the relative Gromov seminorm, analogously to Bavard duality for scl. We give an application to computations of scl in graphs of groups. We also explain how our duality result can be given a purely algebraic interpretation via a relative version of the Hopf formula. Moreover, we show that this leads to a natural generalisation of a result of Calegari on a connection between scl and the rotation quasimorphism. |
| title | Bavard duality for the relative Gromov seminorm |
| topic | Geometric Topology Group Theory 20J05, 57M07, 55M05 |
| url | https://arxiv.org/abs/2305.02149 |