Homology classes of negative square and embedded surfaces in 4-manifolds

M. J. D. Hamilton

doi:10.1112/blms/bdt050

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arXiv · 1301.3733

Homology classes of negative square and embedded surfaces in 4-manifolds

M. J. D. Hamilton

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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.

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BibTeX RIS

M. J. D. Hamilton. 2013-01-16. Homology classes of negative square and embedded surfaces in 4-manifolds. https://doi.org/10.1112/blms%2Fbdt050

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