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 books.google.com Indeed, Pontryagin originally announced that 7c„+2(S") is trivial; apparently
because of a missed framing on the torus. ... But these results on homotopy
groups can be used, through the ThomPontryagin construction, to yield
information about ... 

 books.google.com The construction from maps between spheres to manifolds and back is called the
PontryaginThom construction. It is a standard tool in higher dimensional
topology. To imagine the PontryaginThom construction, I think of a cartoon in
which a ... 

 books.google.com Athanase Papadopoulos  2012  866 pages The PontryaginThom theory, developed half a century ago, provides a link
between classification of manifolds and homotopy ... the basic idea of producing
characteristic classes of smooth fiber bundles via the PontryaginThom
construction. 

 books.google.com xC^gilM)) is obtained (at the space level) as the composite where r(Af") is given
by the PontryaginThom construction using a En$H embedding of M" ( — Mx...
xM) in V. The point is that we could have begun from the //embedding A/C W, ... 

 books.google.com Cl All of the above computations are due to L. Pontryagin and can be read from
his book [Pon55], translated as ... For completeness, even though they were
never obtained using the Pontryagin Thom construction, we also state: Theorem. 

 books.google.com John M. Franks, Conference Board of the Mathematical Sciences  1982  120 pages We can now give the main result of this chapter showing the correspondence of a
connecting manifold with the homotopy class of a relative attaching map via the
Pontryagin Thom construction. Recall that the relative attaching map of a fccell ... 

 books.google.com I︠A︡kov Grigorʹevich Sinaĭ  2003  700 pages Pontryagin graduated from the University of Moscow in 1929, he was then
appointed to the Mechanics and Mathematics Faculty. He became a ... For
example, the essential tool of cobordism theory was the PontryaginThom
construction. 

 books.google.com Vladimir I. Arnold  2004  639 pages In 1976 Andras Szucs, following the idea by M.Gromov, constructed the classified
space for immersions with ... space of plane curves with no horizontal inflection
points generalize the Pontryagin Thom construction in a different way, see [4]. 

 books.google.com Hans U. Boden  2005  347 pages Since V and N both have Spin structures there is a Spin structure on the normal
bundle of V in N. The PontryaginThom construction gives a map N —> T(vvcn)
—> T{^nk), and hence a map N — > MSpin(n—k). If k is large, we suspend by ... 

 books.google.com Alejandro Adem, Jesús González, Guillermo Pastor  2006  191 pages The Euler Characteristic We want to associate to a space F a map <j>(F) : S" — >
S" for some n such that the degree of <j>(F) is the euler characteristic of F. If F is a
closed manifold, we can utilize the PontryaginThom construction as follows. 

 