## A characterization of virtually embedded subsurfaces in $3$-manifolds

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**369**(2017), 1237-1264 Request permission

## 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.## References

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## Additional Information

**Yi Liu**- Affiliation: Department of Mathematics 253-27, California Institute of Technology, Pasadena, California 91125
- Address at time of publication: Beijing International Center for Mathematical Research, No. 5 Yiheyuan Road, Haidian District, Peking University, Beijing 100871, People’s Republic of China
- MR Author ID: 945775
- Email: liuyi@math.pku.edu.cn
- Received by editor(s): October 28, 2014
- Received by editor(s) in revised form: February 23, 2015, and March 26, 2015
- Published electronically: May 2, 2016
- Additional Notes: This work was partially supported by NSF grant DMS-1308836
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**369**(2017), 1237-1264 - MSC (2010): Primary 57M05
- DOI: https://doi.org/10.1090/tran/6707
- MathSciNet review: 3572272