On the semicontinuity of the mod 2 spectrum of hypersurface singularities

TL;DR

This paper proves the semicontinuity of the mod 2 spectrum of isolated hypersurface singularities using topological methods, linking Seifert forms, signatures, and cobordism inequalities.

Contribution

It introduces a purely topological proof of semicontinuity for the mod 2 spectrum, connecting link invariants with hypersurface singularity properties.

Findings

Proves semicontinuity of the mod 2 spectrum using topological tools.

Establishes connections between Seifert forms, signatures, and singularity spectra.

Extends previous work on link cobordisms to hypersurface singularities.

Abstract

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.