Lipschitz homotopy groups of the Heisenberg groups
- Wenger, Stefan Département de Mathématiques, Université de Fribourg, Switzerland
- Young, Robert Department of Mathematics, University of Toronto, Canada
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01.02.2014
Published in:
- Geometric and Functional Analysis. - 2014, vol. 24, no. 1, p. 387–402
English
Lipschitz and horizontal maps from an n-dimensional space into the (2n + 1)-dimensional Heisenberg group Hn are abundant, while maps from higher-dimensional spaces are much more restricted. DeJarnette-Hajłasz-Lukyanenko-Tyson constructed horizontal maps from S to Hn which factor through n-spheres and showed that these maps have no smooth horizontal fillings. In this paper, however, we build on an example of Kaufman to show that these maps sometimes have Lipschitz fillings. This shows that the Lipschitz and the smooth horizontal homotopy groups of a space may differ. Conversely, we show that any Lipschitz map Sk→H1 factors through a tree and is thus Lipschitz null-homotopic if k≥2 .
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 210093
- DOI 10.1007/s00039-014-0264-9
- Persistent URL
- https://folia.unifr.ch/unifr/documents/303656
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