Exotic 4-manifolds with signature zero
Geometric Topology
2024-04-23 v3 Differential Geometry
Symplectic Geometry
Abstract
We produce infinitely many distinct irreducible smooth 4-manifolds homeomorphic to #(2m+1)(CP^2 # -CP^2) and #(2n+1)(S^2 x S^2), respectively, for each m>3 and n>4. These provide the smallest exotic closed simply connected 4-manifolds with signature zero known to date, and in each one of these homeomorphism classes, we get minimal symplectic 4-manifolds. Our novel exotic 4-manifolds are derived from fairly special small Lefschetz fibrations we build via positive factorizations in the mapping class group, with spin and non-spin monodromies.
Cite
@article{arxiv.2305.10908,
title = {Exotic 4-manifolds with signature zero},
author = {R. Inanc Baykur and Noriyuki Hamada},
journal= {arXiv preprint arXiv:2305.10908},
year = {2024}
}
Comments
28 pages, 17 figures in color. Addendum 2 in v3 features smaller exotic signature zero 4-manifolds, with non-trivial pi1