Standard barbell pseudo-isotopies with single-eye Cerf diagrams generate all vanishing-first-Hatcher-Wagoner-invariant pseudo-isotopies for n greater than or equal to 6, with explicit formulas and 4D immersed generalizations.
Concordance spaces, higher simple-homotopy theory, and applications
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Cerf Diagrams and Hatcher-Wagoner Invariants for Barbell Maps
Standard barbell pseudo-isotopies with single-eye Cerf diagrams generate all vanishing-first-Hatcher-Wagoner-invariant pseudo-isotopies for n greater than or equal to 6, with explicit formulas and 4D immersed generalizations.