Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric approach towards stable homotopy groups of spheres. The
  Kervaire invariant II   The notion of the geometrical $\Z/2 \oplus \Z/2$--control of
self-intersection of a skew-framed immersion and the notion of the $\Z/2 \oplus
\Z/4$-structure (the cyclic structure) on the self-intersection manifold of a
$\D_4$-framed immersion are introduced. It is shown that a skew-framed
immersion $f:M^{\frac{3n+q}{4}} \looparrowright \R^n$, $0 < q <<n$ (in the
$\frac{3n}{4}+\epsilon$-range) admits a geometrical $\Z/2 \oplus \Z/2$--control
if the characteristic class of the skew-framing of this immersion admits a
retraction of the order $q$, i.e. there exists a mapping $\kappa_0:
M^{\frac{3n+q}{4}} \to \RP^{\frac{3(n-q)}{4}}$, such that this composition $I
\circ \kappa_0: M^{\frac{3n+q}{4}} \to \RP^{\frac{3(n-q)}{4}} \to \RP^{\infty}$
is the characteristic class of the skew-framing of $f$. Using the notion of
$\Z/2 \oplus \Z/2$-control we prove that for a sufficiently great $n$,
$n=2^l-2$, an arbitrary immersed $\D_4$-framed manifold admits in the regular
cobordism class (modulo odd torsion) an immersion with a $\Z/2 \oplus
\Z/4$-structure. In the last section we present an approach toward the Kervaire
Invariant One Problem.

17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph