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Transactions of the American Mathematical Society

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Contractible 3-manifolds and the double 3-space property


Authors: Dennis J. Garity, Dušan D. Repovš and David G. Wright
Journal: Trans. Amer. Math. Soc. 370 (2018), 2039-2055
MSC (2010): Primary 54E45, 54F65; Secondary 57M30, 57N10
DOI: https://doi.org/10.1090/tran/7035
Published electronically: November 7, 2017
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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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Additional Information

Dennis J. Garity
Affiliation: Department of Mathematics, Oregon State University, Corvallis, Oregon 97331
Email: garity@math.oregonstate.edu

Dušan D. Repovš
Affiliation: Faculty of Education, and Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia 1000
Email: dusan.repovs@guest.arnes.si

David G. Wright
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email: wright@math.byu.edu

DOI: https://doi.org/10.1090/tran/7035
Keywords: Contractible 3-manifold, open 3-manifold, Whitehead Link, defining sequence, geometric index, McMillan contractible 3-manifold, Gabai Link
Received by editor(s): December 12, 2015
Received by editor(s) in revised form: July 21, 2016
Published electronically: November 7, 2017
Additional Notes: The first and second authors were supported in part by the Slovenian Research Agency grant BI-US/15-16-029. The first author was supported in part by the National Science Foundation grant DMS0453304. The first and third authors were supported in part by the National Science Foundation grant DMS0707489. The second author was supported in part by the Slovenian Research Agency grants P1-0292, JL-7025, and J1-6721.
Article copyright: © Copyright 2017 American Mathematical Society

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