Georgia Institute of Technology College of Sciences

Two prominent questions in low dimensional topology are: which knots are slice, and which $\mathbb{Q}$-homology $S^3$'s bound $\mathbb{Q}$-homology $B^4$'s? These questions are connected by a theorem that states if a knot $K$ in $S^3$ is slice, then the 2-fold branch cover of $S^3$ over $K$ bounds a $\mathbb{Q}$-homology $B^4$. In this talk we introduce a generalization of $\chi$-sliceness of links to the rational homology context, generalize the earlier theorem to state that for a rationally $\chi$-slice link $L$, for all sufficiently large primes $p$, the $p$-fold cyclic branch cover of $S^3$ over $L$ bounds a $\mathbb{Q}$-homology $B^4$, and examine a connection to a number-theoretic obstruction on the Alexander polynomial.