Median quasimorphisms on CAT(0) cube complexes and their cup products
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909502452793344 |
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| author | Brück, Benjamin Fournier-Facio, Francesco Loeh, Clara |
| author_facet | Brück, Benjamin Fournier-Facio, Francesco Loeh, Clara |
| contents | Cup products provide a natural approach to access higher bounded cohomology groups. We extend vanishing results on cup products of Brooks quasimorphisms of free groups to cup products of median quasimorphisms, i.e., Brooks-type quasimorphisms of group actions on CAT(0) cube complexes. In particular, we obtain such vanishing results for groups acting on trees and for right-angled Artin groups. Moreover, we outline potential applications of vanishing results for cup products in bounded cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_05811 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Median quasimorphisms on CAT(0) cube complexes and their cup products Brück, Benjamin Fournier-Facio, Francesco Loeh, Clara Group Theory Geometric Topology Cup products provide a natural approach to access higher bounded cohomology groups. We extend vanishing results on cup products of Brooks quasimorphisms of free groups to cup products of median quasimorphisms, i.e., Brooks-type quasimorphisms of group actions on CAT(0) cube complexes. In particular, we obtain such vanishing results for groups acting on trees and for right-angled Artin groups. Moreover, we outline potential applications of vanishing results for cup products in bounded cohomology. |
| title | Median quasimorphisms on CAT(0) cube complexes and their cup products |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2209.05811 |