Abstract
We provide a sufficient condition for the nontriviality of the Lipschitz homotopy group of the Heisenberg group, πmLip(ℍn), in terms of properties of the classical homotopy group of the sphere, πm(Sn). As an application we provide a new simplified proof of the fact that (Formula presented), and we prove a new result that (Formula presented) for n = 1,2,. The last result is based on a new generalization of the Hopf invariant. We also prove that Lipschitz mappings are not dense in the Sobolev space W1,p(M, ℍ2n) when dim M ≥ 4n and 4n-1 ≤ p < 4n.
Original language | English (US) |
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Pages (from-to) | 245-268 |
Number of pages | 24 |
Journal | Geometric and Functional Analysis |
Volume | 24 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2014 |
Keywords
- 55Q25
- 55Q40
- Primary 53C17
- Secondary 46E35
ASJC Scopus subject areas
- Analysis
- Geometry and Topology