Homology classes of negative square and embedded surfaces in 4-manifolds
Geometric Topology
2019-03-05 v2
Abstract
Let X be a simply-connected closed oriented 4-manifold and A an embedded surface of genus g and negative self-intersection -N. We show that for fixed genus g there is an upper bound on N if the homology class of A is divisible or characteristic. In particular, for genus zero, there is a lower bound on the self-intersection of embedded spheres in these kinds of homology classes. This question is related to a problem from the Kirby list.
Cite
@article{arxiv.1301.3733,
title = {Homology classes of negative square and embedded surfaces in 4-manifolds},
author = {M. J. D. Hamilton},
journal= {arXiv preprint arXiv:1301.3733},
year = {2019}
}
Comments
7 pages; to appear in Bull. Lond. Math. Soc