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 Tr. Mat. Inst. Steklova, 2004, Volume 247, Pages 151–158 (Mi tm14)

On Eversion of Spheres

I. Maleshicha, P. E. Pushkar'b, D. Repovša

a University of Ljubljana
b Independent University of Moscow

Abstract: The celebrated Smale–Hirsch classification of immersions allows one to obtain several nice applications of algebraic topology to differential topology. Unfortunately, these applications have yet to be presented in books or survey papers either in Russian or in English. The purpose of this paper is to expose the simplest and most fundamental of these applications: the Smale–Kaiser theorem on the dimension of spheres that can be turned inside out, the Haefliger–Hirsch classification of immersions by means of equivariant maps, and its corollary concerning embeddings of highly connected manifolds (in particular, of spheres).

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English version:
Proceedings of the Steklov Institute of Mathematics, 2004, 247, 135–142

Bibliographic databases:
UDC: 515.162.6

Citation: I. Maleshich, P. E. Pushkar', D. Repovš, “On Eversion of Spheres”, Geometric topology and set theory, Collected papers. Dedicated to the 100th birthday of professor Lyudmila Vsevolodovna Keldysh, Tr. Mat. Inst. Steklova, 247, Nauka, MAIK «Nauka/Inteperiodika», M., 2004, 151–158; Proc. Steklov Inst. Math., 247 (2004), 135–142

Citation in format AMSBIB
\Bibitem{MalPusRep04} \by I.~Maleshich, P.~E.~Pushkar', D.~Repov{\v s} \paper On Eversion of Spheres \inbook Geometric topology and set theory \bookinfo Collected papers. Dedicated to the 100th birthday of professor Lyudmila Vsevolodovna Keldysh \serial Tr. Mat. Inst. Steklova \yr 2004 \vol 247 \pages 151--158 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm14} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2168167} \zmath{https://zbmath.org/?q=an:1108.57022} \transl \jour Proc. Steklov Inst. Math. \yr 2004 \vol 247 \pages 135--142