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On the classification of fake lens spaces
-
Tibor Macko
and
Christian Wegner
Published/Copyright:
May 31, 2010
Abstract
In the first part of the paper we present a topological classification of fake lens spaces of dimension ≥ 5 whose fundamental group is the cyclic group of order any N ≥ 2. The classification is stated in terms of the simple structure sets in the sense of surgery theory. The results use and extend the results of Wall and others in the cases N = 2 and N odd and the results of the authors of the present paper in the case N= 2K.
In the second part we study the suspension map between the simple structure sets of lens spaces of different dimensions. As an application we obtain an inductive geometric description of the torsion invariants of fake lens spaces.
Received: 2009-02-07
Revised: 2009-11-05
Published Online: 2010-05-31
Published in Print: 2011-September
© de Gruyter 2011
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Articles in the same Issue
- Quantum unique ergodicity of Eisenstein series on the Hilbert modular group over a totally real field
- On the self-intersection cycle of surfaces and some classical formulas for their secant varieties
- Wolff potentials and the 3-d wave operator
- Statistics for low-lying zeros of symmetric power L-functions in the level aspect
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