Proc Natl Acad Sci U S A
October 2018
Given a diagram for a trisection of a 4-manifold X, we describe the homology and the intersection form of X in terms of the three subgroups of [Formula: see text] generated by the three sets of curves and the intersection pairing on [Formula: see text] This includes explicit formulas for the second and third homology groups of X as well an algorithm to compute the intersection form. Moreover, we show that all [Formula: see text]-trisections admit "algebraically trivial" diagrams.
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