A simple class of infinitely many absolutely exotic manifolds

Abstract

We show that the smooth $4$-manifold $M$ obtained by attaching a $2$-handle to $B^4$ along a certain knot $K\subset \partial B^4$ admits infinitely many absolutely exotic copies $M_n$, $n=0,1,\mathrm{2..}$, such that each copy $M_n$ is obtained by attaching $2$-handle to a fixed compact smooth contractible manifold $W$ along the iterates $f^n(c)$ of a knot $c\subset \partial W$ by a diffeomorphism $f:\partial W\to \partial W$. This generalizes the example in author's 1991 paper, which corresponds to $n=1$ case.

5 pages 8 figures

References in corpus (2)

• Tight small Seifert fibered manifolds with $e_0=-2$
• On infinite order corks

Cited by in corpus (1)

• Homotopy $4$-spheres associated to an infinite order loose cork