On the geometric boundaries of hyperbolic 4-manifolds

Abstract

We provide, for hyperbolic and flat 3-manifolds, obstructions to bounding hyperbolic 4-manifolds, thus resolving in the negative a question of Farrell and Zdravkovska.

8 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol4/paper5.abs.html

References in corpus (1)

• All flat manifolds are cusps of hyperbolic orbifolds

Cited by in corpus (33)

• Hyperbolic four-manifolds with one cusp
• Peaks in the Hartle-Hawking Wave Function from Sums over Topologies
• Peripheral separability and cusps of arithmetic hyperbolic orbifolds
• Some hyperbolic three-manifolds that bound geometrically
• All flat manifolds are cusps of hyperbolic orbifolds
• Hyperbolic four-manifolds, colourings and mutations
• Pinched smooth hyperbolization
• The complement of the figure-eight knot geometrically bounds
• (0,2) Dualities and the 4-Simplex
• A geometrically bounding hyperbolic link complement
• Eta invariants for flat manifolds
• Orientable hyperbolic 4-manifolds over the 120-cell
• Cusps of arithmetic orbifolds
• Embedding non-arithmetic hyperbolic manifolds
• Many cusped hyperbolic 3-manifolds do not bound geometrically
• Counting cusped hyperbolic 3-manifolds that bound geometrically
• The signature of cusped hyperbolic 4-manifolds
• Cusped hyperbolic 3-manifolds: canonically CAT(0) with CAT(0) spines
• Cusps of Hilbert modular varieties
• Arithmetic cusp shapes are dense
• Cusps and Commensurability Classes of Hyperbolic 4-Manifolds
• Geometrically bounding 3-manifold, volume and Betti number
• Relative cubulation of relative strict hyperbolization
• A hyperbolic counterpart to Rokhlin's cobordism theorem
• Eta Invariant and Conformal Cobordism
• Complements of tori in ${\#}_{2k}{S}^2\times S^2$ that admit a hyperbolic structure
• Some cusp-transitive hyperbolic 4-manifolds
• An almost flat manifold with a cyclic or quaternionic holonomy group bounds
• The eta function and eta invariant of ${\mathbb{Z}}_{2^r}$-manifolds
• Regularity of the eta function on manifolds with cusps
• Problems on Bieberbach groups and flat manifolds
• Flat manifolds, harmonic spinors, and eta invariants
• Controlling manifold covers of orbifolds