The double $n$–space property for contractible $n$–manifolds

Abstract

Motivated by a recent paper of Gabai (J. Topol. 4 (2011) 529–534) on the Whitehead contractible 3–manifold, we investigate contractible manifolds $M^n$ which decompose or split as $M^n=A{\cup }_{C}B$ with $A,B,C\approx {ℝ}^n$ or $A,B,C\approx {\mathbb{B}}^n$. Of particular interest to us is the case $n=4$. Our main results exhibit large collections of 4–manifolds that split in this manner.