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Sbornik: Mathematics, 2016, Volume 207, Issue 11, Pages 1562–1581
DOI: https://doi.org/10.1070/SM8679 (Mi sm8679) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On some problems related to the Hilbert-Smith conjecture

A. N. Dranishnikov

Department of Mathematics, University of Florida, Gainesville, FL, USA
English version PDF (581 kB) Citations (1) Russian version article
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DOI: https://doi.org/10.1070/SM8679
Abstract: The Hilbert-Smith conjecture claims that if a compact group $G$ acts freely on a manifold, then it is a Lie group. For a finite-dimensional orbit space a reduction of the Hilbert-Smith conjecture to certain other problems in geometric topology is presented; in these the key problem is the existence of an essential sequence of lens spaces of increasing dimension.
Bibliography: 52 titles.
Keywords: free action of a group, lens spaces, $K$-theory, completely regular maps.
Funding agency Grant number
National Science Foundation DMS-1304627
This research was supported by the NSF (grant no. DMS-1304627).
Received: 22.02.2016 and 19.06.2016
Bibliographic databases:
Document Type: Article
UDC: 515.124+515.127+515.16
MSC: Primary 55M30; Secondary 53C23, 57N65
Language: English
Original paper language: Russian
Citation: A. N. Dranishnikov, “On some problems related to the Hilbert-Smith conjecture”, Sb. Math., 207:11 (2016), 1562–1581
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v207/i11/p82
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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