Many cusped hyperbolic 3-manifolds do not bound geometrically

Kolpakov, Alexander; Reid, Alan; Riolo, Stefano

doi:10.1090/proc/14573

Many cusped hyperbolic 3-manifolds do not bound geometrically
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by Alexander Kolpakov, Alan W. Reid and Stefano Riolo PDF

Proc. Amer. Math. Soc. 148 (2020), 2233-2243

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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