Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lipschitz homotopy groups of the Heisenberg groups   Lipschitz and horizontal maps from an $n$-dimensional space into the
$(2n+1)$-dimensional Heisenberg group $\H^n$ are abundant, while maps from
higher-dimensional spaces are much more restricted.
DeJarnette-Haj{\l}asz-Lukyanenko-Tyson constructed horizontal maps from $S^k$
to $\H^n$ 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 $S^k\to \H^1$ factors
through a tree and is thus Lipschitz null-homotopic if $k\ge 2$.

4
The categories of this paper are: cond-mat
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The categories of this paper are: econ
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas