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abstract: 'We consider double plumbings of two disk bundles over spheres. We calculate the Heegaard–Floer homology with its absolute grading of the boundary of such a plumbing. Given a closed smooth 4–manifold $X$ and a suitable pair of classes in $H_{2}(X)$, we investigate when this pair of classes may be represented by a configuration of surfaces in $X$ whose regular neighborhood is a double plumbing of disk bundles over spheres. Using similar methods we study single plumbings of two disk bundles over spheres inside $X$.'
address: |
    Faculty of Education\
    University of Ljubljana\
    Kardeljeva ploščad 16\
    1000 Ljubljana, Slovenia
author:
- Eva Horvat
bibliography:
- 'lit1.bib'
date: 'July 18, 2013'
title: Double plumbings of disk bundles over spheres
---

[Introduction]{} Given a smooth closed connected 4–manifold $X$ and a finite set of classes $C\subset H_{2}(X)$, an important question is what is the simplest configuration of surfaces in $X$ representing $C$. By simple we mean that each class should be represented by a surface of low genus and that the surfaces should have a low number of geometric intersections. Since it is always possible to remove cancelling pairs of intersection points by increasing the genus of a surface, both properties 