Geodesic
On fake lens spaces with fundamental group of order a power of 2
Macko, Tibor1 ; Wegner, Christian2
1Mathematisches Institut, Universität Münster, Einsteinstraße 62, Münster D-48149, Germany, Matematický Ústav SAV, Štefánikova 49, Bratislava SK-81473, Slovakia
2Mathematisches Institut, Universität Münster, Einsteinstraße 62, Münster D-48149, Germany
Algebraic and Geometric Topology, Tome 9 (2009) no. 3, pp. 1837-1883
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We present a classification of fake lens spaces of dimension ≥ 5 which have as fundamental group the cyclic group of order N = 2K, which extends the results of Wall and others in the case N = 2.

DOI : 10.2140/agt.2009.9.1837
Keywords: lens space, structure set, $\rho$–invariant, normal invariants, surgery

Macko, Tibor  1   ; Wegner, Christian  2

1 Mathematisches Institut, Universität Münster, Einsteinstraße 62, Münster D-48149, Germany, Matematický Ústav SAV, Štefánikova 49, Bratislava SK-81473, Slovakia
2 Mathematisches Institut, Universität Münster, Einsteinstraße 62, Münster D-48149, Germany 
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Macko, Tibor; Wegner, Christian. On fake lens spaces with fundamental group of order a power of 2. Algebraic and Geometric Topology, Tome 9 (2009) no. 3, pp. 1837-1883. doi: 10.2140/agt.2009.9.1837

[1] M F Atiyah, I M Singer, The index of elliptic operators. III, Ann. of Math. $(2)$ 87 (1968) 546

[2] P E Conner, E E Floyd, Differentiable periodic maps, Ergebnisse der Math. und ihrer Grenzgebiete 33, Academic Press (1964)

[3] I Hambleton, L R Taylor, A guide to the calculation of the surgery obstruction groups for finite groups, from: "Surveys on surgery theory, Vol. 1" (editors S Cappell, A Ranicki, J Rosenberg), Ann. of Math. Stud. 145, Princeton Univ. Press (2000) 225

[4] W Lück, A basic introduction to surgery theory, from: "Topology of high-dimensional manifolds, No. 1, 2 (Trieste, 2001)" (editors F T Farrell, L Göttsche, W Lück), ICTP Lect. Notes 9, Abdus Salam Int. Cent. Theoret. Phys. (2002) 1

[5] T Macko, C Wegner, On the classification of fake lens spaces

[6] I Madsen, R J Milgram, The classifying spaces for surgery and cobordism of manifolds, Annals of Math. Studies 92, Princeton University Press (1979)

[7] S López De Medrano, Involutions on manifolds, Ergebnisse der Math. und ihrer Grenzgebiete 59, Springer (1971)

[8] J Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72 (1966) 358

[9] J W Morgan, D P Sullivan, The transversality characteristic class and linking cycles in surgery theory, Ann. of Math. $(2)$ 99 (1974) 463

[10] T Petrie, The Atiyah–Singer invariant, the Wall groups $L_{n}(\pi , 1)$, and the function $(te^{x}+1)/(te^{x}-1)$, Ann. of Math. $(2)$ 92 (1970) 174

[11] A A Ranicki, A composition formula for manifold structures

[12] A A Ranicki, Algebraic $L$–theory and topological manifolds, Cambridge Tracts in Math. 102, Cambridge Univ. Press (1992)

[13] C T C Wall, Surgery on compact manifolds, Math. Surveys and Monogr. 69, Amer. Math. Soc. (1999)

[14] C M Young, Normal invariants of lens spaces, Canad. Math. Bull. 41 (1998) 374

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