Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tempered currents and the cohomology of the remote fiber of a real
  polynomial map   Let $p:R^n\to R$ be a polynomial map. Consider the complex
$S'\Omega^*(\RR^n)$ of tempered currents on $R^n$ with the twisted differential
$d_p=d-dp$ where $d$ is the usual exterior differential and $dp$ stands for the
exterior multiplication by $dp$. Let $t\in R$ and let $F_t=p^{-1}(t)$. In this
paper we prove that the reduced cohomology $\tilda H^k(F_t;C)$ of $F_t$ is
isomorphic to $H^{k+1}(S'\Omega^*(\RR^n),d_p)$ in the case when $p$ is
homogeneous and $t$ is any positive real number. We conjecture that this
isomorphism holds for any polynomial $p$, for $t$ large enough (we call the
$F_t$ for $t >> 0$ the remote fiber of $p$) and we prove this conjecture for
polynomials that satisfy certain technical condition. The result is analogous
to that of A. Dimca and M. Saito, who give a similar (algebraic) way to compute
the reduced cohomology of the generic fiber of a complex polynomial.

4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex