Abstract:
There are several combinatorial models to describe knotted surfaces in $S^4$, but they remain difficult to handle in general. Cut-diagrams are an attempt to provide an efficient and user-friendly tool to, at least, capture all the homotopy information of the complement of a knotted surface. They can be seen as a higher dimensional version of welded knot theory. In my talk, I will introduce them and show how they can be used to provide algorithmically computable invariants of knotted surfaces. Applications to link-maps (immersions of surfaces with only self-singularities) shall also be discussed.
Link for connecting to the seminar: https://mian.ktalk.ru/j1xwg956wc7a "PIN code": The number of homotopy classes of maps from the Russian word 쬄 to the Russian word ¨Æ (where a word is understood as the subset of the plane formed by its letters)
