Configurations of surfaces in 4-manifolds

Gilmer, Patrick M.

doi:10.1090/S0002-9947-1981-0603768-7

Configurations of surfaces in $4$-manifolds
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by Patrick M. Gilmer

Trans. Amer. Math. Soc. 264 (1981), 353-380

DOI: https://doi.org/10.1090/S0002-9947-1981-0603768-7

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Abstract:

We consider collections of surfaces $\{ {F_i}\}$ smoothly embedded, except for a finite number of isolated singularities, self-intersections, and mutual intersections, in a $4$-manifold $M$. A small $3$-sphere about each exceptional point will intersect these surfaces in a link. If $[{F_i}] \in {H_2}(M)$ are linearly dependent modulo a prime power, we find lower bounds for $\Sigma$ genus $({F_i})$ in terms of the $[{F_i}]$, and invariants of the links that describe the exceptional points.

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