Smooth structures on four-manifolds with finite cyclic fundamental groups
Geometric Topology
2024-06-14 v1 Differential Geometry
Abstract
For each nonnegative integer m we show that any closed, oriented topological four-manifold with fundamental group Z_{4m+2} and odd intersection form, with possibly seven exceptions, either admits no smooth structure or admits infinitely many distinct smooth structures up to diffeomorphism. Moreover, we construct infinite families of non-complex irreducible fake projective planes with diverse fundamental groups.
Cite
@article{arxiv.2406.09007,
title = {Smooth structures on four-manifolds with finite cyclic fundamental groups},
author = {R. Inanc Baykur and Andras I. Stipsicz and Zoltan Szabo},
journal= {arXiv preprint arXiv:2406.09007},
year = {2024}
}
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32 pages