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Russian Mathematical Surveys, 2000, Volume 55, Issue 6, Pages 1085–1129
DOI: https://doi.org/10.1070/rm2000v055n06ABEH000334 (Mi rm334) 		 
This article is cited in 103 scientific papers (total in 103 papers)

Asymptotic topology

A. N. Dranishnikov

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (475 kB) Citations (103)
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DOI: https://doi.org/10.1070/rm2000v055n06ABEH000334
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.
Received: 29.12.1999
Russian version:
Uspekhi Matematicheskikh Nauk, 2000, Volume 55, Issue 6(336), Pages 71–116
DOI: https://doi.org/10.4213/rm334
Bibliographic databases:
Document Type: Article
UDC: 515.12
MSC: Primary 54F45, 54C55; Secondary 54E35, 18B30, 54D35, 54D40, 20H15
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 103 articles:
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    References:76
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