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Homotopy classification
of $4$–manifolds whose fundamental group is dihedral
Daniel Kasprowski, John Nicholson and Benjamin Ruppik |
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Algebraic & Geometric Topology 22 (2022) 2915–2949
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Abstract |
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We show that the homotopy type of a finite oriented Poincaré –complex is determined by its quadratic –type provided its fundamental group is finite and has a dihedral Sylow –subgroup. By combining with results of Hambleton and Kreck and Bauer, this applies in the case of smooth oriented –manifolds whose fundamental group is a finite subgroup of . An important class of examples are elliptic surfaces with finite fundamental group. |
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Keywords
Whitehead’s Gamma group, homotopy classification of
4–manifolds, Poincaré complexes
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Mathematical Subject Classification
Primary: 57K40
Secondary: 16E05, 57N65, 57P10
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References |
Publication
Received: 7 January 2021
Revised: 1 July 2021
Accepted: 14 July 2021
Published: 13 December 2022
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Authors |
| Daniel Kasprowski | |
| Mathematisches Institut Rheinische Friedrich-Wilhelms-Universität Bonn Germany |
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| John Nicholson | |
| Department of Mathematics Imperial College London London United Kingdom |
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| Benjamin Ruppik | |
| Max-Planck-Institut für
Mathematik Bonn Germany |
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