Kasprowski, D;
Nicholson, J;
Ruppik, B;
(2022)
Homotopy classification of 4-manifolds whose fundamental group is dihedral.
Algebraic & Geometric Topology
, 22
(6)
pp. 2915-2949.
10.2140/agt.2022.22.2915.
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Abstract
We show that the homotopy type of a finite oriented Poincaré 4 –complex is determined by its quadratic 2 –type provided its fundamental group is finite and has a dihedral Sylow 2 –subgroup. By combining with results of Hambleton and Kreck and Bauer, this applies in the case of smooth oriented 4 –manifolds whose fundamental group is a finite subgroup of SO ( 3 ) . An important class of examples are elliptic surfaces with finite fundamental group.
| Type: | Article |
|---|---|
| Title: | Homotopy classification of 4-manifolds whose fundamental group is dihedral |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.2140/agt.2022.22.2915 |
| Publisher version: | https://doi.org/10.2140/agt.2022.22.2915 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Whitehead’s Gamma group, homotopy classification of 4–manifolds, Poincaré complexes |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10136829 |
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