Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Configurations of surfaces in $ 4$-manifolds

Author: Patrick M. Gilmer
Journal: Trans. Amer. Math. Soc. 264 (1981), 353-380
MSC: Primary 57Q35; Secondary 57M25, 57R95
MathSciNet review: 603768
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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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Article copyright: © Copyright 1981 American Mathematical Society