The Double n-Space Property for Contractible n-Manifolds

Abstract

Motivated by a recent paper of Gabai on the Whitehead contractible 3-manifold, we investigate contractible manifolds $M^n$ which decompose or split as $M^n=A{\cup }_{C}B$ where $A,B,C\approx {\mathbb{R}}^n$ 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.

This is a more concise version of the author's dissertation arXiv:1502.03154

References in corpus (1)

• Contractible 3-manifolds and the double 3-space property

Cited by in corpus (1)

• On uniqueness of end sums and 1-handles at infinity