论文标题
图形的Upsilon不变和同源性同源气缸的同源性cobordism群
Upsilon invariant for graphs and the homology cobordism group of homology cylinders
论文作者
论文摘要
Upsilon是Ozsváth，Stipsicz和Szabó定义的平稳结合的同态。在本文中，我们为在理性同源球中的一个嵌入式图定义了UPSILON的概括。我们表明，我们的不变将引起同源性同源性圆柱体的同型同态，并介绍一些应用。为了定义这种不变，我们使用缠结的浮子同源性。我们将缠结平面同源性的相对等级提高到绝对等级（对于某些缠结），并证明了串联公式。
Upsilon is a homomorphism on the smooth concordance group of knots defined by Ozsváth, Stipsicz and Szabó. In this paper, we define a generalization of upsilon for a family of embedded graphs in rational homolog spheres. We show that our invariant will induce a homomorphism on the homology cobordism group of homology cylinders, and present some applications. To define this invariant, we use tangle Floer homology. We lift relative gradings on tangle Floer homology to absolute gradings (for certain tangles) and prove a concatenation formula for it.
