  We use purely topological methods to prove the semicontinuity of the mod 2
spectrum of local isolated hypersurface singularities in $\mathbb{C}^{n+1}$,
using Seifert forms of high-dimensional non-spherical links, the
Levine--Tristram signatures and the generalized Murasugi--Kawauchi inequality
obtained in earlier work for cobordisms of links.
