I was intrigued by this machine which uses light emitting diodes to make gel nail polish set.
It turns out that the trick is that they emit ultra-violet light.
https://www.miladypro.com/home/b/nails/archive/2017/11/10/the-difference-between-uv-and-led-nail-dryers#:~:text=LED%20lights%20work%20similarly%2C%20but,cure%20much%20faster%20than%20UV.
The UV has the energy to get the molecules in the gel to turn into long polymer molecules - molecules made of repeating identical sections. This makes them turn from small molecules in a liquid to hard molecules in a solid. No mention of whether or not it is a cross-linking polymer but a little consultation of Google suggests it probably is.
Sadly not my nails! Thanks, Lydia.
