Survey of recent results on the topology of the set of $\mathbb{RC}$-singular points of a real submanifold in a complex manifold

A point of a real (smooth) submanifold in a complex manifold is said to be $\mathbb{RC}$-singular if the dimension of the complex tangent space at this point is greater than the minimum possible for these dimensions of the manifold and the submanifold. Starting with the history of who and why studied the topological structure of the set of $\mathbb{RC}$-singular points, we shall describe a series of recent results in this direction. For example, Kasuya and Takase proved in 2016 that every homologous to zero embedded circle in a closed three-dimensional manifold is the set of $\mathbb{RC}$-singular points for some embedding of this manifold in $\mathbb{C}^3$.