In this note we show that there exist cusped hyperbolic 3-mani-folds 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.
Many cusped hyperbolic 3-manifolds do not bound geometrically / Kolpakov A.; Reid A.W.; Riolo S.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - ELETTRONICO. - 148:5(2020), pp. 2233-2243. [10.1090/proc/14573]
Many cusped hyperbolic 3-manifolds do not bound geometrically
Riolo S.
2020
Abstract
In this note we show that there exist cusped hyperbolic 3-mani-folds 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.File in questo prodotto:
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