Cusps and Commensurability Classes of Hyperbolic 4-Manifolds

Connor Sell

doi:10.2140/agt.2023.23.3805

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arXiv · 2109.12172

Cusps and Commensurability Classes of Hyperbolic 4-Manifolds

Connor Sell

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Abstract

There are six orientable, compact, flat 3-manifolds that can occur as cusp cross-sections of hyperbolic 4-manifolds. This paper provides criteria for exactly when a given commensurability class of arithmetic hyperbolic 4-manifolds contains a representative with a given cusp type. In particular, for three of the six cusp types, we provide infinitely many examples of commensurability classes that contain no manifolds with cusps of the given type; no such examples were previously known for any cusp type.

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BibTeX RIS

Connor Sell. 2021-09-24. Cusps and Commensurability Classes of Hyperbolic 4-Manifolds. https://doi.org/10.2140/agt.2023.23.3805

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