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Uspekhi Mat. Nauk, 2000, Volume 55, Issue 6(336), Pages 71–116 (Mi umn334)  

This article is cited in 78 scientific papers (total in 78 papers)

Asymptotic topology

A. N. Dranishnikov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: In this paper we study the similarity between local topology and its global analogue, so-called asymptotic topology. In the asymptotic case, the notions of dimension, cohomological dimension, and absolute extensor are introduced and some basic facts about them are proved. The Higson corona functor establishing a connection between macro- and micro-topology is considered. A relationship between problems of general asymptotic topology and the Novikov conjecture on higher signatures is discussed. Some new results concerning the Novikov conjecture and other related conjectures are presented.

DOI: https://doi.org/10.4213/rm334

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English version:
Russian Mathematical Surveys, 2000, 55:6, 1085–1129

Bibliographic databases:

UDC: 515.12
MSC: Primary 54F45, 54C55; Secondary 54E35, 18B30, 54D35, 54D40, 20H15
Received: 29.12.1999

Citation: A. N. Dranishnikov, “Asymptotic topology”, Uspekhi Mat. Nauk, 55:6(336) (2000), 71–116; Russian Math. Surveys, 55:6 (2000), 1085–1129

Citation in format AMSBIB
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\paper Asymptotic topology
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\yr 2000
\vol 55
\issue 6(336)
\pages 71--116
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\pages 1085--1129
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