|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
Homotopy classification
of $4$–manifolds whose fundamental group is dihedral
Daniel Kasprowski, John Nicholson and Benjamin Ruppik |
|
Algebraic & Geometric Topology 22 (2022) 2915–2949
|
Abstract |
|
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. |
Keywords
Whitehead’s Gamma group, homotopy classification of
4–manifolds, Poincaré complexes
|
Mathematical Subject Classification
Primary: 57K40
Secondary: 16E05, 57N65, 57P10
|
References |
Publication
Received: 7 January 2021
Revised: 1 July 2021
Accepted: 14 July 2021
Published: 13 December 2022
|
Authors |
| Daniel Kasprowski | |
| Mathematisches Institut Rheinische Friedrich-Wilhelms-Universität Bonn Germany |
|
| John Nicholson | |
| Department of Mathematics Imperial College London London United Kingdom |
|
| Benjamin Ruppik | |
| Max-Planck-Institut für
Mathematik Bonn Germany |
|
