Published February 2017
| Submitted
Journal Article
Open
A characterization of virtually embedded subsurfaces in 3-manifolds
- Creators
- Liu, Yi
Chicago
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Abstract
This paper introduces the spirality character of the almost fiber part for a closed essentially immersed subsurface of a closed orientable aspherical 3-manifold, which generalizes an invariant due to Rubinstein and Wang. The subsurface is virtually embedded if and only if the almost fiber part is aspiral, and in this case, the subsurface is virtually a leaf of a taut foliation. Besides other consequences, examples are exhibited that nongeometric 3-manifolds with no Seifert fibered pieces may contain essentially immersed but not virtually embedded closed subsurfaces.
Additional Information
© 2016 American Mathematical Society. Received by the editors October 28, 2014 and, in revised form, February 23, 2015 and March 26, 2015. This work was partially supported by NSF grant DMS-1308836. The author thanks Yi Ni and Alan Reid for valuable communications. The author would also like to thank the anonymous referee for pointing out some incorrect formulations in Proposition 3.1 and Formula 7.2 in an earlier manuscript.Attached Files
Submitted - 1406.4674.pdf
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Additional details
- Eprint ID
- 73132
- Resolver ID
- CaltechAUTHORS:20161222-093226423
- NSF
- DMS-1308836
- Created
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2016-12-22Created from EPrint's datestamp field
- Updated
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2021-11-11Created from EPrint's last_modified field