I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2007, VOLUME 13, NUMBER 8, PAGES 17-41
Geometric approach to stable homotopy groups of spheres.
Kervaire invariants. II
P. M. Akhmet'ev
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We present an approach to the Kervaire-invariant-one problem.
The notion of the geometric -control of self-intersection of
a skew-framed immersion and the notion of the -structure on the self-intersection
manifold of a -framed
immersion are introduced.
It is shown that a skew-framed immersion , (in the
admits a geometric -control if the characteristic class
of the skew-framing of this immersion admits a retraction of the
i.e., there exists a mapping
such that this composition
is the characteristic class of the skew-framing of .
Using the notion of -control, we prove that for
a sufficiently large , , an arbitrary
manifold admits in the regular cobordism
class (modulo odd torsion) an immersion with a -structure.
Last modified: June 13, 2008