

Geometric Topology Seminar
July 20, 2017 15:00–17:00, Moscow, Steklov Mathematical Institute, room 534






$\Delta$link homotopy of links in $S^3$ and invariants of link maps in $S^4$
S. A. Melikhov^{} 
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Abstract:
In 2003, Nakanishi and Ohyama obtained a classification of $2$component links up to $\Delta$link homotopy.
Namely, they are classified by the linking number and the generalized SatoLevine invariant. Using Kirk's invariant of link maps $S^2\sqcup S^2\to S^4$ and its variation due to Koschorke, we obtain a simple proof of the Nakanishi–Ohyama theorem, and also its version for string links. We also prove that $3$component links that are trivial up to link homotopy are classified up to weak $\Delta$link homotopy by $\bar\mu$invariants of length $\le 4$. The proof uses a computation of the image of Koschorke's $\tilde\beta$invariant of link maps $S^2\sqcup S^2\sqcup S^2\to S^4$ (which is strictly stronger than GuiSong Li's version of Kirk's invariant). This computation in is turn based on Yasuhara's results about $\Delta$link homotopy. This talk is based on joint work with Yuka Kotorii.
Materials:
extended_abstract.pdf (108.9 Kb)
Language: English

