Cerf Diagrams and Hatcher-Wagoner Invariants for Barbell Maps

Xiayu Tan

For a half-unknotted implanted $(i,n-i)$-barbell $\beta ={\beta }_{i,n-i}$ in $M^n$, we construct two specific pseudo-isotopies, which we denote by standard barbell pseudo-isotopies, both resu…