On self-intersection invariants

TL;DR

This paper demonstrates the equivalence of Hatcher-Quinn and Wall invariants for self-transverse immersions and explores their properties using normal bordism theory.

Contribution

It establishes an isomorphism between the Hatcher-Quinn and Wall invariants, unifying their descriptions for self-transverse immersions.

Findings

Hatcher-Quinn and Wall invariants coincide for self-transverse immersions

Constructed an explicit isomorphism between the invariants' target groups

Applied normal bordism theory to analyze invariants in codimension one

Abstract

We prove that the Hatcher-Quinn and Wall invariants of a self-transverse immersion $f\co N^n\imm M^{2n}$ coincide. That is, we construct an isomorphism between their target groups which carries one onto the other. We also employ methods of normal bordism theory to investigate the Hatcher-Quinn invariant of an immersion $f\co N^n\imm M^{2n-1}$.