A conjectural chain model for positive $S^1$-equivariant symplectic homology of star-shaped toric domains in ${\mathbb{C}}^2$

Abstract

For any star-shaped toric domain in ${\mathbb{C}}^2$, we define a filtered chain complex which conjecturally computes positive $S^1$-equivariant symplectic homology of the domain. Assuming this conjecture, we show that the limit ${\lim }_{k\to \infty }{c}_k^{\mathrm{GH}}(X)/k$ exists for any star-shaped toric domain $X\subset {\mathbb{C}}^2$, where $c_k^{\mathrm{GH}}$ denotes the $k$-th Gutt-Hutchings capacity.

arXiv comment13 pages