论文标题
固定点的固定点浮点同源性的产品和相关物，dehn twist
Product and Coproduct on Fixed Point Floer Homology of Positive Dehn Twists
论文作者
论文摘要
我们在单个Dehn Twist上的固定点浮点同源性上计算产品和副型结构，但要受到一些轻微的拓扑限制。我们表明，所得的产品和相关结构取决于扭曲区域补体的摩尔斯同源性的产物和相关性，以及$ t^*s^1 $的符号同源性的某些乘积和共同构造结构。该计算是通过直接枚举$ j- $ holomorthic部分进行的：我们使用局部能量不平等来表明某些假定的霍明型部分不存在，我们使用粘合构造以及一些莫尔斯 - 摩特理论来构造我们无法排除的部分。
We compute the product and coproduct structures on the fixed point Floer homology of iterations on the single Dehn twist, subject to some mild topological restrictions. We show that the resulting product and coproduct structures are determined by the product and coproduct on Morse homology of the complement of the twist region, together with certain sectors of product and coproduct structures on the symplectic homology of $T^*S^1$. The computation is done via a direct enumeration of $J-$holomorphic sections: we use a local energy inequality to show that some of the putative holomorphic sections do not exist, and we use a gluing construction plus some Morse-Bott theory to construct the sections we could not rule out.
