The link volume of 3-manifolds is not multiplicative under coverings
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- by Jair Remigio–Juárez
- Proc. Amer. Math. Soc. 144 (2016), 4075-4079
- DOI: https://doi.org/10.1090/proc/13008
- Published electronically: February 12, 2016
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Abstract:
We obtain an infinite family of $3-$manifolds $\{{M}_n\}_{n\in \mathbb {N}}$ and an infinite family of coverings $\{\varphi _n:\tilde {M}_n\to M_{n}\}_{n\in \mathbb {N}}$ with covering degrees unbounded and satisfying that $\operatorname {LinkVol}[\tilde {M}]=\operatorname {LinkVol}[M].$ This shows that link volume of 3-manifolds is not well behaved under covering maps, in particular, it is not multiplicative, and gives a negative answer to a question posed in a work of Rieck and Yamashita, namely, how good is the bound $\operatorname {LinkVol}[\tilde {M}]\leq q \operatorname {LinkVol}[M]$, when $\tilde {M}$ is a $q$-fold covering of $M$?References
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Bibliographic Information
- Jair Remigio–Juárez
- Affiliation: División Académica de Ciencias Básicas, Universidad Juárez Autónoma de Tabasco, Km. 1 Carr. Cunduacán-Jalpa de Méndezm, Cunduacán, Tab. 86690, Mexico
- Email: jair.remigio@ujat.mx
- Received by editor(s): September 24, 2014
- Received by editor(s) in revised form: September 8, 2015, and October 21, 2015
- Published electronically: February 12, 2016
- Communicated by: Martin Scharlemann
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 4075-4079
- MSC (2010): Primary 57M10, 57M12, 57M25, 57M27
- DOI: https://doi.org/10.1090/proc/13008
- MathSciNet review: 3513562