This article is cited in 15 papers

Embedding of compacta, stable homotopy groups of spheres, and singularity theory

P. M. Akhmet'ev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: In this survey new applications of homotopy theory and singularity theory to geometric and differential topology are considered. The solution of R. Daverman's problem on the embedding of a sphere-like compactum in Euclidean space is obtained. Applications to the theory of pseudo-isotopies and to the topology of low-dimensional manifolds are found.

UDC: 515.142

MSC: Primary 55Q45, 58K05; Secondary 57M50, 57N37, 57N35, 57Q35, 57Q60, 57R15

Received: 21.12.1998

DOI: 10.4213/rm290

 English version: Russian Mathematical Surveys, 2000, 55:3, 405–462

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