Many cusped hyperbolic 3-manifolds do not bound geometrically

Alexander Kolpakov; Alan W. Reid; Stefano Riolo

doi:10.1090/proc/14573

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arXiv · 1811.05509

Many cusped hyperbolic 3-manifolds do not bound geometrically

Alexander Kolpakov·Alan W. Reid·Stefano Riolo

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Abstract

In this note, we show that there exist cusped hyperbolic $3$-manifolds that embed geodesically, but cannot bound geometrically. Thus, being a geometric boundary is a non-trivial property for such manifolds. Our result complements the work by Long and Reid on geometric boundaries of compact hyperbolic $4$-manifolds, and by Kolpakov, Reid and Slavich on embedding arithmetic hyperbolic manifolds.

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Alexander Kolpakov, Alan W. Reid, Stefano Riolo. 2018-11-13. Many cusped hyperbolic 3-manifolds do not bound geometrically. https://doi.org/10.1090/proc%2F14573

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