Contractible 3-manifolds and the double 3-space property
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- by Dennis J. Garity, Dušan D. Repovš and David G. Wright PDF
- Trans. Amer. Math. Soc. 370 (2018), 2039-2055 Request permission
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.References
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Additional Information
- Dennis J. Garity
- Affiliation: Department of Mathematics, Oregon State University, Corvallis, Oregon 97331
- MR Author ID: 195931
- Email: garity@math.oregonstate.edu
- Dušan D. Repovš
- Affiliation: Faculty of Education, and Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia 1000
- MR Author ID: 147135
- ORCID: 0000-0002-6643-1271
- Email: dusan.repovs@guest.arnes.si
- David G. Wright
- Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
- MR Author ID: 191898
- Email: wright@math.byu.edu
- 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.
- © Copyright 2017 American Mathematical Society
- 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
- MathSciNet review: 3739201