A simple class of infinitely many absolutely exotic manifolds

TL;DR

This paper constructs infinitely many absolutely exotic smooth structures on certain 4-manifolds obtained by attaching 2-handles, generalizing a previous example and demonstrating rich exotic phenomena in 4-dimensional topology.

Contribution

It introduces a new method to generate infinitely many absolutely exotic 4-manifolds by iterating diffeomorphisms on boundary knots, extending prior constructions.

Findings

Constructed infinitely many absolutely exotic manifolds

Generalized previous 1991 example to a broader class

Demonstrated rich exotic phenomena in 4-manifold topology

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 $M_n$, $n=0,1,2..$, 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.