Contractible 3-manifolds and the double 3-space property

Dennis J. Garity; Dušan D. Repovš; David G. Wright

doi:10.1090/tran/7035

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arXiv · 1711.05043

Contractible 3-manifolds and the double 3-space property

Dennis J. Garity·Dušan D. Repovš·David G. Wright

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Abstract

Gabai showed that the Whitehead manifold is the union of two submanifolds each of which is homeomorphic to $\mathbb R^3$ and whose intersection is again homeomorphic to $\mathbb R^3$. Using a family of generalizations of the Whitehead Link, we show that there are uncountably many contractible 3-manifolds with this double 3-space property. Using a separate family of generalizations of the Whitehead Link and using an extension of interlacing theory, we also show that there are uncountably many contractible 3-manifolds that fail to have this property.

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BibTeX RIS

Dennis J. Garity, Dušan D. Repovš, David G. Wright. 2017-11-14. Contractible 3-manifolds and the double 3-space property. https://doi.org/10.1090/tran%2F7035

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