Geodesic
Torsions and intersection forms of 4-manifolds from trisection diagrams
Canadian journal of mathematics, Tome 74 (2022) no. 2, pp. 527-549

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DOI

Gay and Kirby introduced trisections, which describe any closed, oriented, smooth 4-manifold X as a union of three 4-dimensional handlebodies. A trisection is encoded in a diagram, namely three collections of curves in a closed oriented surface $\Sigma $, guiding the gluing of the handlebodies. Any morphism $\varphi $ from $\pi _1(X)$ to a finitely generated free abelian group induces a morphism on $\pi _1(\Sigma )$. We express the twisted homology and Reidemeister torsion of $(X;\varphi )$ in terms of the first homology of $(\Sigma ;\varphi )$ and the three subspaces generated by the collections of curves. We also express the intersection form of $(X;\varphi )$ in terms of the intersection form of $(\Sigma ;\varphi )$.
DOI : 10.4153/S0008414X20000863
Mots-clés : 4-manifold trisections, intersection forms, Reidemeister torsion 
Florens, Vincent; Moussard, Delphine. Torsions and intersection forms of 4-manifolds from trisection diagrams. Canadian journal of mathematics, Tome 74 (2022) no. 2, pp. 527-549. doi: 10.4153/S0008414X20000863
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     title = {Torsions and intersection forms of 4-manifolds from trisection diagrams},
     journal = {Canadian journal of mathematics},
     pages = {527--549},
     year = {2022},
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