论文标题
圆锥和二元性上的乘法结构
Multiplicative structures on cones and duality
论文作者
论文摘要
我们启动锥体上的乘法结构的研究，并表明漂浮式延续图的锥自然适合此框架。我们将其应用于Rabinowitz Floer同源性和协同学上的乘法结构的新描述，并给出了与两者相关的Poincaré二元定理的新证明。基础代数结构承认了两个新的化身，我们都在研究和比较：一方面，$ a_2^+$ - 花序的$ a_2^+$ - 代数的结构$ \ nathcal {a} $ floer链条的{a} $，另一方$ \ MATHCAL {a}^\ vee $和从$ \ Mathcal {a}^\ vee $到$ \ MATHCAL {a} $的连续图。
We initiate the study of multiplicative structures on cones and show that cones of Floer continuation maps fit naturally in this framework. We apply this to give a new description of the multiplicative structure on Rabinowitz Floer homology and cohomology, and to give a new proof of the Poincaré duality theorem which relates the two. The underlying algebraic structure admits two incarnations, both new, which we study and compare: on the one hand the structure of $A_2^+$-algebra on the space $\mathcal{A}$ of Floer chains, and on the other hand the structure of $A_2$-algebra involving $\mathcal{A}$, its dual $\mathcal{A}^\vee$ and a continuation map from $\mathcal{A}^\vee$ to $\mathcal{A}$.
