We relate the quantum Steenrod square to Seidel’s equivariant pair-of-pants product for open convex symplectic manifolds that are either monotone or exact, using an equivariant version of the PSS isomorphism. We define continuation maps between different Hamiltonians in $\mathbb{Z}/2$-equivariant Floer cohomology, and prove expected properties of them. We prove a symplectic Cartan relation for the equivariant pair-of-pants product, pointing out the difficulties in stating it. We give a nonvanishing result for the equivariant pair-of-pants product for some elements of $S{H}^{\ast }(T^{\ast }{S}^n)$. We finish by calculating the symplectic square for the negative line bundles $M=\text{Tot}({𝒪}(-1)\to {ℂ\mathbb{P}}^m)$, proving an equivariant version of a result due to Ritter.

我们使用 PSS 同构的等变版本，将量子 Steenrod 方块与单调或精确的开凸辛流形的 Seidel 等变裤子积联系起来。我们定义了不同哈密顿量之间的延续映射$\mathbb{Z}/\mathrm{2个}$-等变 Floer 上同调，并证明它们的预期性质。我们证明了等变裤子产品的辛 Cartan 关系，指出了陈述它的困难。对于某些元素，我们给出了等变裤子产品的非零结果$\mathrm{小号}{H}^{＊}({吨}^{＊}{\mathrm{小号}}^n)$. 我们通过计算负线束的辛平方来完成$米=\text{托特}({𝒪}(-\mathrm{1个})\to {ℂ\mathbb{P}}^{米})$，证明了 Ritter 结果的等变版本。