Lipschitz Homotopy Groups of the Heisenberg Groups |
| |
Authors: | Stefan Wenger Robert Young |
| |
Institution: | 1. Département de Mathématiques, Université de Fribourg, Chemin du Musée 23, 1700, Fribourg, Switzerland 2. Department of Mathematics, University of Toronto, 40 St. George St., Room 6290, Toronto, ON, M5S 2E4, Canada
|
| |
Abstract: | Lipschitz and horizontal maps from an n-dimensional space into the (2n + 1)-dimensional Heisenberg group ${\mathbb{H}^n}$ are abundant, while maps from higher-dimensional spaces are much more restricted. DeJarnette-Haj?asz-Lukyanenko-Tyson constructed horizontal maps from S k to ${\mathbb{H}^n}$ 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 ${S^k \to \mathbb{H}^1}$ factors through a tree and is thus Lipschitz null-homotopic if ${k \geq 2}$ . |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|