I will outline a construction of multi-parameter families of arcs in 4-manifolds, and explain how some spectral sequence calculations can show their nontriviality. This relies on work of many people in the field of embedding calculus.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/13837