The Schneiderman-Teichner invariant applied to immersions arising from link maps in $S^4$

Abstract

It is shown that Schneiderman and Teichner's invariant $\tau$ detects the example due to Kirk of a link map $f:S^2_+\cup S^2_-\to S^4$ for which the restricted map $f|S^2_+:S^2_+\to S^4-f(S^2_-)$ has vanishing Wall self-intersection but is not homotopic to an embedding.