The Arf invariant of proper links in solid tori (Q917978)

An n-component link in \(S^ 3\) is called ``proper'', if each component has an even linking number with the rest of the link. Two links \(\ell\) and \(\ell (m)\) in a solid torus V are T-related if they are carried into each other by an m-fold meridional twist of V. The author proves relations between the Arf-invariants of \(\ell\) and \(\ell (m)\) dependent on the winding number of \(\ell\) in V. The work of Robertello on the Arf- invariant is used and a relation of Murakami between the Arf-invariant and the Jones polynomial at i.