Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-products of rationally elliptic spaces and inequalities between the
  ranks of homotopy and homology groups   We give a survey on recent results on inequalities between the ranks of
homotopy and cohomology groups (resp., graded components of mixed Hodge
structures on these groups) of rationally elliptic spaces (resp.,
quasi-projective varieties which are rationally elliptic). We also discuss a
refinement of these results describing a new invariant of rationally elliptic
spaces allowing to compare the ranks of homotopy and homology groups. This
invariant is a specialization of an invariant $r\left ( P(t),Q(t);\varepsilon
\right )$ of a pair $\left (P(t),Q(t) \right )$ of polynomials with
non-negative integer coefficients, describing the range of variable $r$ such
that $rP(t)<Q(t)^r$ for all $t \ge \varepsilon$. This range is related to the
classical Lambert W-function $W(z)$.

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The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con