The double n–space property for contractible n–manifolds

Sparks, Peter

doi:10.2140/agt.2018.18.2131

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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

DOI: 10.2140/agt.2018.18.2131

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 $A, B, C \approx B^{n}$ . 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

Mathematical Subject Classification 2010

Primary: 57N13

Secondary: 57N15

References

Publication

Received: 20 October 2016

Revised: 3 January 2018

Accepted: 26 January 2018

Published: 26 April 2018

Authors

Peter Sparks
Department of Mathematics, Statistics and Computer Science Marquette University Milwaukee, WI United States

Volume 18, issue 4 (2018)