Disoriented homology and double branched covers

Abstract This paper provides a convenient and practical method to compute the homology intersection pairing of branched double cover 4-ball. To projections links in 3-ball, surfaces 4-ball into boundary sphere, we associate sequence groups, called disoriented homology. We show that is isomorphic link or surface. define on first group surface this equal cover. These results generalize work Gordon Litherland, for embedded 3-sphere, arbitrary also give generalization signature formula Gordon–Litherland general setting. Our are underpinned by theorem describing handle decomposition codimension-2 submanifold n -ball, which generalizes previous Akbulut–Kirby others.