A cork of the rational surface with the second Betti number 9

TL;DR

This paper presents the first explicit example of a cork in a specific 4-manifold with second Betti number 9, advancing understanding of smooth structures in 4-dimensional topology.

Contribution

It provides the first explicit cork example in a manifold with second Betti number 9, the smallest known for such explicit constructions.

Findings

First explicit cork example in a manifold with b2=9

Establishes the smallest known second Betti number for explicit corks

Advances the study of smooth structures in 4-manifolds

Abstract

We provide the first explicit example of a cork of $\mathbf{CP}^2 \# 8\overline{\mathbf{CP}^2}$. This result gives the current smallest second Betti number of a standard simply-connected closed $4$-manifold for which an explicit cork has been found.