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Quantum Steenrod squares and the equivariant pair-of-pants in symplectic cohomology
Journal of Topology and Analysis ( IF 0.5 ) Pub Date : 2021-05-10 , DOI: 10.1142/s1793525321500369
Nicholas Wilkins 1, 2
Affiliation  

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 /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 SH(TSn). We finish by calculating the symplectic square for the negative line bundles M=Tot(𝒪(1)m), proving an equivariant version of a result due to Ritter.



中文翻译:

量子 Steenrod 方块和辛上同调中的等变裤子

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/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小号H(小号n). 我们通过计算负线束的辛平方来完成=托特(𝒪(1个)),证明了 Ritter 结果的等变版本。

更新日期:2021-05-10
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