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We apply mapping class group techniques and trisections to study intersectionforms of smooth 4-manifolds. Johnson defined a well-known homomorphism from theTorelli group of a compact surface. Morita later showed that every homology3-sphere can be obtained from the standard Heegaard decomposition of $S^3$ byregluing according to a map in the kernel of this homomorphism. We prove ananalogous result for trisections of 4-manifolds. Specifically, if $X$ and $Y$admit handle decompositions without 1- or 3-handles and have isomorphicintersection forms, then a trisection of $Y$ can be obtained from a trisectionof $X$ by cutting and regluing by an element of the Johnson kernel. We alsodescribe how invariants of homology 3-spheres can be applied, via this result,to obstruct intersection forms of smooth 4-manifolds. As an application, we usethe Casson invariant to recover Rohlin's Theorem on the signature of spin4-manifolds.

Trisections, intersection forms and the Torelli group