arXiv:2611.14691v1 Announce Type: new Abstract: We compute the cylindrical contact homology chain complex associated with a monotone toric domain in $\mathbb{R}^4$. The chain complexes allow us to compute the cylindrical contact homology capacities associated with monotone toric domains with one or two inflection points. These capacities are conjecturally equal to the Gutt-Hutchings capacities defined using $S^1$-equivariant symplectic homology. Using our results, we find embedding obstructions between toric domains.
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