#### Volume 18, issue 4 (2018)

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The double $n\mkern-1.5mu$–space property for contractible $n\mkern-1.5mu$–manifolds

### Peter Sparks

Algebraic & Geometric Topology 18 (2018) 2131–2149
##### 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.

##### Keywords
Mazur manifold, jester's manifold, dunce hat, jester's hat, pseudohandle
Primary: 57N13
Secondary: 57N15