论文标题
关于一致性不变的注释Upsilon和Phi
A note on the concordance invariants Upsilon and phi
论文作者
论文摘要
DAI，HOM，Stoffregen和Truong定义了一个和解的家庭$φ_J$。 HOM先前给出的零不变但非零的EPSILON不变的结的示例也具有非零的PHI不变性。我们表明，在平滑的一致性组中有无限的许多这样的结线性独立。在相反的方向上，我们建立了无限独立结的家族，而零PHI不变但非零UPSILON不变。我们还为圆环结的Phi不变性提供了递归公式。
Dai, Hom, Stoffregen and Truong defined a family of concordance invariants $φ_j$. The example of a knot with zero Upsilon invariant but nonzero epsilon invariant previously given by Hom also has nonzero phi invariant. We show there are infinitely many such knots that are linearly independent in the smooth concordance group. In the opposite direction, we build infinite families of linearly independent knots with zero phi invariant but nonzero Upsilon invariant. We also give a recursive formula for the phi invariant of torus knots.
