From letter-quasimorphisms to angle structures and spectral gaps for scl
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913456860430336 |
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| author | Marchand, Alexis |
| author_facet | Marchand, Alexis |
| contents | We give a new geometric proof of a theorem of Heuer showing that, in the presence of letter-quasimorphisms (which are analogues of real-valued quasimorphisms with image in free groups), and in particular in RAAGs, there is a sharp lower bound of 1/2 for stable commutator length. Our approach is to show that letter-quasimorphisms give rise to negatively curved angle structures on admissible surfaces. This generalises Duncan and Howie's proof of the 1/2-lower bound in free groups, and can also be seen as a version of Bavard duality for letter-quasimorphisms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_13856 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From letter-quasimorphisms to angle structures and spectral gaps for scl Marchand, Alexis Group Theory Geometric Topology 20F65, 20F67, 57M07 We give a new geometric proof of a theorem of Heuer showing that, in the presence of letter-quasimorphisms (which are analogues of real-valued quasimorphisms with image in free groups), and in particular in RAAGs, there is a sharp lower bound of 1/2 for stable commutator length. Our approach is to show that letter-quasimorphisms give rise to negatively curved angle structures on admissible surfaces. This generalises Duncan and Howie's proof of the 1/2-lower bound in free groups, and can also be seen as a version of Bavard duality for letter-quasimorphisms. |
| title | From letter-quasimorphisms to angle structures and spectral gaps for scl |
| topic | Group Theory Geometric Topology 20F65, 20F67, 57M07 |
| url | https://arxiv.org/abs/2402.13856 |