Invariants of free knots valued in free groups

This talk is a part of the project of creating “non-commutative” invariants in topology. The main idea is to replace “characteristic classes” of moduli spaces with “characteristic loops”. We discuss “the last stage” of the talk devoted to the abstract objects we get in the end: the free knots, an discuss their invariants valued in free groups.
These invariants allow one to detect easily mutations, invertibility, and other phenomena.