Geodesic
Cusps and commensurability classes of hyperbolic 4–manifolds
Sell, Connor1
1 Department of Mathematics, Rice University, Houston, TX, United States
Algebraic and Geometric Topology, Tome 23 (2023) no. 8, pp. 3805-3834

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

There are six orientable compact flat 3–manifolds that can occur as cusp cross-sections of hyperbolic 4–manifolds. We provide 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.

DOI : 10.2140/agt.2023.23.3805
Keywords: hyperbolic manifold, $4$–manifold, cusp, arithmetic, quadratic form, hyperbolic geometry

Sell, Connor 1

1 Department of Mathematics, Rice University, Houston, TX, United States 
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Sell, Connor. Cusps and commensurability classes of hyperbolic 4–manifolds. Algebraic and Geometric Topology, Tome 23 (2023) no. 8, pp. 3805-3834. doi: 10.2140/agt.2023.23.3805

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