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


Author: Yi Liu
Journal: Trans. Amer. Math. Soc. 369 (2017), 1237-1264
MSC (2010): Primary 57M05
DOI: https://doi.org/10.1090/tran/6707
Published electronically: May 2, 2016
Erratum: Trans. Amer. Math. Soc. 369 (2017), no. 2, 1513-1515
MathSciNet review: 3572272
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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.


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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
Email: liuyi@math.pku.edu.cn

DOI: https://doi.org/10.1090/tran/6707
Keywords: Spirality character, virtually embedded subsurface, suspension flow
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
Article copyright: © Copyright 2016 American Mathematical Society