On atoroidal and hyperbolic cohomology classes
- We study hyperbolic cohomology classes in the general context of simplicial complexes and prove homological invariance statements for them. We relate the existence of hyperbolic cohomology classes to the non-amenability of the fundamental group. In degree two we clarify the relation between bounded, hyperbolic and atoroidal classes. This leads to both an application to symplectically atoroidal manifolds, and an improved understanding of recent attempts to find atoroidal classes.
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| Author: | M. Brunnbauer, D. Kotschick, Lukas Schönlinner |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1110535 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/111053 |
| ISSN: | 0166-8641OPAC |
| Parent Title (English): | Topology and its Applications |
| Publisher: | Elsevier BV |
| Type: | Article |
| Language: | English |
| Date of first Publication: | 2024/01/17 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2024/01/31 |
| Tag: | Geometry and Topology |
| Volume: | 344 |
| First Page: | 108830 |
| DOI: | https://doi.org/10.1016/j.topol.2024.108830 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Differentialgeometrie | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY-NC-ND 4.0: Creative Commons: Namensnennung - Nicht kommerziell - Keine Bearbeitung (mit Print on Demand) |
