Computes the monopole Floer homology and twisting involution of the complexity-2 protocork boundary, and constructs h-cobordisms of arbitrarily large Morgan-Szabó complexity between exotic pairs of closed 1-connected 4-manifolds.
The equivalence of lattice and Heegaard Floer homology
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abstract
We prove N\'{e}methi's conjecture: if $Y$ is a 3-manifold which is the boundary of a plumbing of a tree of disk bundles over $S^2$, then the lattice homology of $Y$ coincides with the Heegaard Floer homology of $Y$. We also give a conjectural description of the $H_1(Y)/\mathrm{Tors}$ action when $b_1(Y)>0$.
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On $h$-cobordisms of complexity $2$
Computes the monopole Floer homology and twisting involution of the complexity-2 protocork boundary, and constructs h-cobordisms of arbitrarily large Morgan-Szabó complexity between exotic pairs of closed 1-connected 4-manifolds.