Lipschitz homotopy groups of the Heisenberg groups

Wenger, Stefan; Young, Robert

doi:10.1007/s00039-014-0264-9

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Journal article

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

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