Quasimorphisms on the group of density preserving diffeomorphisms of the Möbius band
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909577798221824 |
|---|---|
| author | Kim, KyeongRo Maruyama, Shuhei |
| author_facet | Kim, KyeongRo Maruyama, Shuhei |
| contents | The existence of quasimorphisms on groups of homeomorphisms of manifolds has been extensively studied under various regularity conditions, such as smooth, volume-preserving, and symplectic. However, in this context, nothing is known about groups of `area'-preserving diffeomorphisms on non-orientable manifolds.
In this paper, we initiate the study of groups of density-preserving diffeomorphisms on non-orientable manifolds.
Here, the density is a natural concept that generalizes volume without concerning orientability. We show that the group of density-preserving diffeomorphisms on the Möbius band admits countably many unbounded quasimorphisms which are linearly independent. Along the proof, we show that groups of density preserving diffeomorphisms on compact, connected, non-orientable surfaces with non-empty boundary are weakly contractible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18466 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasimorphisms on the group of density preserving diffeomorphisms of the Möbius band Kim, KyeongRo Maruyama, Shuhei Geometric Topology Dynamical Systems Group Theory Symplectic Geometry The existence of quasimorphisms on groups of homeomorphisms of manifolds has been extensively studied under various regularity conditions, such as smooth, volume-preserving, and symplectic. However, in this context, nothing is known about groups of `area'-preserving diffeomorphisms on non-orientable manifolds. In this paper, we initiate the study of groups of density-preserving diffeomorphisms on non-orientable manifolds. Here, the density is a natural concept that generalizes volume without concerning orientability. We show that the group of density-preserving diffeomorphisms on the Möbius band admits countably many unbounded quasimorphisms which are linearly independent. Along the proof, we show that groups of density preserving diffeomorphisms on compact, connected, non-orientable surfaces with non-empty boundary are weakly contractible. |
| title | Quasimorphisms on the group of density preserving diffeomorphisms of the Möbius band |
| topic | Geometric Topology Dynamical Systems Group Theory Symplectic Geometry |
| url | https://arxiv.org/abs/2412.18466 |