2024/06/18 by Lee, Jaewon · 1 citation
#57K10 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2406.12761
It is well known that there are many 2-torsion elements in the classical knot concordance group. On the other hand, it is not known if there is any torsion element in the rational knot concordance group C_ℚ. Cha defined the algebraic rational concordance group AC_ℚ, an analogue of the classical algebraic concordance group, and showed that AC_ℚ≅ℤ^∞⊕ℤ2^∞⊕ℤ4^∞. The knots that represent 2-torsions in AC_ℚ potentially have order 2 in C_ℚ. In this paper, we provide an obstruction for knots of order 2 in AC_ℚ from being of finite order in C_ℚ. Moreover, we give a family consisting of such knots that generates an infinite rank subgroup of C_ℚ. We also note that Cha proved that in higher dimensions, the algebraic rational concordance order is the same as the rational knot concordance order. Our obstruction is based on the localized von Neumann ρ-invariant.