Homotopy classification of 4-manifolds whose fundamental group is dihedral

Kasprowski, Daniel; Nicholson, John; Ruppik, Benjamin

doi:10.2140/agt.2022.22.2915

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Homotopy classification of 4-manifolds whose fundamental group is dihedral

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Ruppik, Benjamin
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.2140/agt.2022.22.2915
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https://doi.org/10.48550/arXiv.2011.03520
(Preprint)

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Kasprowski-Nicholson-Ruppik_Homotopy classification of 4-manifolds whose fundamental group is dihedral_2022.pdf
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Citation

Kasprowski, D., Nicholson, J., & Ruppik, B. (2022). Homotopy classification of 4-manifolds whose fundamental group is dihedral. Algebraic & Geometric Topology, 22(6), 2915-2949. doi:10.2140/agt.2022.22.2915.

Cite as: https://hdl.handle.net/21.11116/0000-0009-FFDE-F

Abstract

We show that the homotopy type of a finite oriented Poincar\'{e} 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-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.