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arXiv · 1507.00139

Bounds on genus and configurations of embedded surfaces in 4-manifolds

Hokuto Konno
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Abstract

For several embedded surfaces with zero self-intersection number in 4-manifolds, we show that an adjunction-type genus bound holds for at least one of the surfaces under certain conditions. For example, we derive certain adjunction inequalities for surfaces embedded in $m\mathbb{CP}^2\# n(-\mathbb{CP}^2)$ ($m, n \geq 2$). The proofs of these results are given by studying a family of Seiberg-Witten equations.

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Hokuto Konno. 2015-07-01. Bounds on genus and configurations of embedded surfaces in 4-manifolds. https://doi.org/10.1112/jtopol%2Fjtw021

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