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

Motivated by a recent paper of Gabai (J. Topol. 4 (2011) 529–534) on the Whitehead contractible 3–manifold, we investigate contractible manifolds Mn which decompose or split as Mn = A CB with A,B,C n or A,B,C Bn. Of particular interest to us is the case n = 4. Our main results exhibit large collections of 4–manifolds that split in this manner.

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Mazur manifold, jester's manifold, dunce hat, jester's hat, pseudohandle
Mathematical Subject Classification 2010
Primary: 57N13
Secondary: 57N15
Received: 20 October 2016
Revised: 3 January 2018
Accepted: 26 January 2018
Published: 26 April 2018
Peter Sparks
Department of Mathematics, Statistics and Computer Science
Marquette University
Milwaukee, WI
United States