We use the branched cover construction and ideas from connected Floer homology to define concordance invariants of knot in $S^3$. Calculations can be performed for double branched covers, in which case the invariants are trivial for alternating and torus knots and non-trivial for some pretzel knots. This allows us to derive some independence results in the smooth concordance group of knots.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/9096