论文标题
塞伯格（Seiberg）的浮子光谱和接触结构
Seiberg-Witten Floer Spectra and Contact Structures
论文作者
论文摘要
在本文中，作者定义了配备触点结构的理性同源性3型弹簧的不变性，作为Manolescu（2003）中定义的Seiberg-Witten浮子光谱的共同运动集的元素。 Furthermore, in light of the equivalence established in Lidman & Manolescu (2018a) between the Borel equivariant homology of said spectrum and the Seiberg-Witten Floer homology of Kronheimer & Mrowka (2007), the author shall show that this homotopy theoretic invariant recovers the already well known contact element in the Seiberg-Witten Floer cohomology (vid. e.g. Kronheimer，Mrowka，Ozsváth＆Szabó2007）以自然方式。接下来，在有限覆盖的情况下，考虑了共同体不变性的行为。这种设置自然要求使用Borel Somology eproivariant在甲板转换组方面使用。因此，定义了一种新的模棱两可的触点不变性并研究了其属性。然后在一个具体的示例中计算不变的，在其中，作者证明了它打开了考虑迄今无法访问的情况的可能性。
In this article, the author defines an invariant of rational homology 3-spheres equipped with a contact structure as an element of a cohomotopy set of the Seiberg-Witten Floer spectrum as defined in Manolescu (2003). Furthermore, in light of the equivalence established in Lidman & Manolescu (2018a) between the Borel equivariant homology of said spectrum and the Seiberg-Witten Floer homology of Kronheimer & Mrowka (2007), the author shall show that this homotopy theoretic invariant recovers the already well known contact element in the Seiberg-Witten Floer cohomology (vid. e.g. Kronheimer, Mrowka, Ozsváth & Szabó 2007) in a natural fashion. Next, the behaviour of the cohomotopy invariant is considered in the presence of a finite covering. This setting naturally asks for the use of Borel cohomology equivariant with respect to the group of deck transformations. Hence, a new equivariant contact invariant is defined and its properties studied. The invariant is then computed in one concrete example, wherein the author demonstrates that it opens the possibility of considering scenarios hitherto inaccessible.
