Variations of 4-dimensional twists obtained by an infinite order plug

Abstract

In the previous paper the author defined an infinite order plug $(P,\phi )$ which gives rise to infinite Fintushel-Stern's knot-surgeries. Here, we give two 4-dimensional infinitely many exotic families $Y_n$, $Z_n$ of exotic enlargements of the plug. The families $Y_n$, $Z_n$ have $b_2=3$, $4$ and the boundaries are 3-manifolds with $b_1=1$, $0$ respectively. We give a plug (or g-cork) twist $(P,{\phi }_{p,q})$ producing the 2-bridge knot or link surgery by combining the plug $(P,\phi )$. As a further example, we describe a 4-dimensional twist $(M,\mu )$ between knot-surgeries for two mutant knots. The twisted double concerning $(M,\mu )$ gives a candidate of exotic ${\#}^2{S}^2\times S^2$.

31 pages, 33 figures