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Mat. Sb., 2016, Volume 207, Number 11, Pages 82–104 (Mi msb8679)  

On some problems related to the Hilbert-Smith conjecture

A. N. Dranishnikov

Department of Mathematics, University of Florida, Gainesville, FL, USA

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).


DOI: https://doi.org/10.4213/sm8679

Full text: PDF file (870 kB)
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English version:
Sbornik: Mathematics, 2016, 207:11, 1562–1581

Bibliographic databases:

UDC: 515.124+515.127+515.16
MSC: Primary 55M30; Secondary 53C23, 57N65
Received: 22.02.2016 and 19.06.2016

Citation: A. N. Dranishnikov, “On some problems related to the Hilbert-Smith conjecture”, Mat. Sb., 207:11 (2016), 82–104; Sb. Math., 207:11 (2016), 1562–1581

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