Quasimorphisms on nonorientable surface diffeomorphism groups
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Mitsuaki Kimura
und
Erika Kuno
Abstract
Bowden, Hensel and Webb constructed infinitely many quasimorphisms on the diffeomorphism groups of orientable surfaces. In this paper, we extend their result to nonorientable surfaces. Namely, we prove that the space of nontrivial quasimorphisms
Funding statement: The first author is supported by JSPS KAKENHI Grant Number JP20H00114 and JP24K16921, and JST-Mirai Program Grant Number JPMJMI22G1. The second author is supported by the Foundation of Kinoshita Memorial Enterprise, by a JSPS KAKENHI Grant-in-Aid for Early-Career Scientists, Grant Number 21K13791, and by JST, ACT-X, Grant Number JPMJAX200D.
Acknowledgements
The authors wish to express their great appreciation to Genki Omori for valuable comments on mapping class groups of nonorientable surfaces. The authors are also deeply grateful to Kazuhiro Ichihara for answering their questions about filling curves. The authors would also like to thank Jonathan Bowden for his comments on the genus 2 case.
Communicated by: T. Grundhöfer
References
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© 2025 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Polyhedral combinatorics of bisectors
- Explicit construction of decomposable Jacobians
- Some rigidity results on q-solitons
- Quasimorphisms on nonorientable surface diffeomorphism groups
- On nearly optimal paper Moebius bands
- Desargues’ Theorem in Laguerre Planes
- Simple obstructions and cone reduction
- The Bogomolov–Gieseker–Koseki inequality on surfaces with canonical singularities in arbitrary characteristic
- The simultaneous lattice packing-covering constant of octahedra
- An Abel–Jacobi theorem for metrized complexes of Riemann surfaces
- Exploring the interplay of semistable vector bundles and their restrictions on reducible curves
- Another proof of Segre’s theorem about ovals
Artikel in diesem Heft
- Frontmatter
- Polyhedral combinatorics of bisectors
- Explicit construction of decomposable Jacobians
- Some rigidity results on q-solitons
- Quasimorphisms on nonorientable surface diffeomorphism groups
- On nearly optimal paper Moebius bands
- Desargues’ Theorem in Laguerre Planes
- Simple obstructions and cone reduction
- The Bogomolov–Gieseker–Koseki inequality on surfaces with canonical singularities in arbitrary characteristic
- The simultaneous lattice packing-covering constant of octahedra
- An Abel–Jacobi theorem for metrized complexes of Riemann surfaces
- Exploring the interplay of semistable vector bundles and their restrictions on reducible curves
- Another proof of Segre’s theorem about ovals
