English

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.

Keywords

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