Whitney多边形，符号同调与配边映射
Whitney polygons, symbol homology and cobordism maps
摘要：
利用Whitney多边形的修饰模空间定义了一个新的同调论，我们称之为符号同调。通过修饰不同类型的模空间，我们得到了这种同调论的不同性质以及它们之间的态射。每一种风味都编码了不同类型的Heegaard弗洛尔同调的特性。符号同调之间的态射使我们能够将性质从一个Floer理论推到另一个理论。此外，我们得到了一个新的介绍Heegaard Floer理论，其中映射对应于乘法从右边与适当的元素，我们的符号同调。最后，我们给出了纽结-Floer理论中配边映射的构造，并利用符号同调的工具给出了一个不变性证明。
英文摘要：
We define a new homology theory we call symbol homology by using decorated moduli spaces of Whitney polygons. By decorating different types of moduli spaces we obtain different flavors of this homology theory together with morphisms between them. Each of these flavors encodes the properties of a different type of Heegaard Floer homology. The morphisms between the symbol homologies enable us to push properties from one Floer theory to a different one. Furthermore, we obtain a new presentation of Heegaard Floer theory in which maps correspond to multiplication from the right with suitable elements of our symbol homology. Finally, we present the construction of cobordism maps in knot Floer theories and apply the tools from symbol homology to give an invariance proof.
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