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

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