Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On negatively curved bundles with hyperbolic fibers outside the Igusa
  stable range   We prove that the Teichm\"{u}ller space $\mathcal{T}^{<0}(M)$ of negatively
curved metrics on a hyperbolic manifold $M$ has nontrivial $i$-th rational
homotopy groups for some $i> \dim M$. Moreover, some elements of infinite order
in $\pi_i B\mbox{Diff}(M)$ can be represented by bundles over $S^i$ with
fiberwise negatively curved metrics.

21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics