Calculating the homology and intersection form of a 4-manifold from a trisection diagram

Peter Feller; Michael Klug; Trent Schirmer; Drew Zemke

doi:10.1073/pnas.1717176115

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arXiv · 1711.04762

Calculating the homology and intersection form of a 4-manifold from a trisection diagram

Peter Feller·Michael Klug·Trent Schirmer·Drew Zemke

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Abstract

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 $H_1(\Sigma;\mathbb{Z})$ generated by the three sets of curves and the intersection pairing on the diagram surface $\Sigma$. 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 $(g;k,0,0)$-trisections admit "algebraically trivial" diagrams.

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Peter Feller, Michael Klug, Trent Schirmer, Drew Zemke. 2017-11-13. Calculating the homology and intersection form of a 4-manifold from a trisection diagram. https://doi.org/10.1073/pnas.1717176115

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