On the geometric boundaries of hyperbolic 4-manifolds

DOI10.2140/gt.2000.4.171zbMath0961.57011arXivmath/0007197OpenAlexW2100978647MaRDI QIDQ1583634

Alan W. Reid, Darren D. Long

Publication date: 27 November 2000

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0007197

zbMATH Keywords

totally geodesichyperbolic 3-manifold\(\eta\)-invariantflat manifold

Mathematics Subject Classification ID

General geometric structures on low-dimensional manifolds (57M50) Other types of cobordism (57R90)

Related Items

Peripheral separability and cusps of arithmetic hyperbolic orbifolds ⋮ Hyperbolic four-manifolds with one cusp ⋮ Cusp cross-sections of hyperbolic orbifolds by Heisenberg nilmanifolds. I ⋮ Spectral theory of the Atiyah-Patodi-Singer operator on compact flat manifolds ⋮ Riemannian hyperbolization ⋮ The complement of the figure-eight knot geometrically bounds ⋮ Cusps and commensurability classes of hyperbolic 4-manifolds ⋮ Hyperbolic 24-Cell 4-Manifolds With One Cusp ⋮ Cusps of Hilbert modular varieties ⋮ Geometrically bounding 3-manifolds, volume and Betti numbers ⋮ Regularity of the eta function on manifolds with cusps ⋮ The spectrum of Schrödinger operators and Hodge Laplacians on conformally cusp manifolds ⋮ Eta invariants for flat manifolds ⋮ Integrality of volumes of representations ⋮ Arithmetic cusp shapes are dense ⋮ Aspherical manifolds with relatively hyperbolic fundamental groups. ⋮ The \(\eta\) invariant of the Atiyah-Patodi-Singer operator on compact flat manifolds ⋮ Eta invariant and conformal cobordism ⋮ (0,2) dualities and the 4-simplex ⋮ Problems on Bieberbach groups and flat manifolds ⋮ All flat manifolds are cusps of hyperbolic orbifolds ⋮ Aspherical 4-manifolds of odd Euler characteristic ⋮ Counting cusped hyperbolic 3-manifolds that bound geometrically ⋮ Boundaries of locally conformally flat manifolds in dimensions $4k$ ⋮ Many cusped hyperbolic 3-manifolds do not bound geometrically ⋮ Hyperbolic 4‐manifolds, colourings and mutations ⋮ The eta function and eta invariant of \(\mathbb{Z}_{2^r}\)-manifolds ⋮ Orientable hyperbolic 4-manifolds over the 120-cell ⋮ A geometrically bounding hyperbolic link complement ⋮ Some hyperbolic three-manifolds that bound geometrically ⋮ Infinitely many arithmetic hyperbolic rational homology 3–spheres that bound geometrically

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Do almost flat manifolds bound?
• Volume and bounded cohomology
• Flat Riemannian manifolds are boundaries
• Knots, homology spheres, and contractible 4-manifolds
• The boundary integrand in the formula for the signature and Euler characteristic of a Riemannian manifold with boundary
• All flat three-manifolds appear as cusps of hyperbolic four-manifolds
• Tubular neighborhood of totally geodesic hypersurfaces in hyperbolic manifolds
• Tunnelling with a negative cosmological constant
• An asymptotic formula for the eta invariants of hyperbolic 3-manifolds
• Spectral Asymmetry and Riemannian Geometry
• Spectral asymmetry and Riemannian Geometry. I
• Geometric Invariants for Seifert Fibred 3-Manifolds
• The Volume Spectrum of Hyperbolic 4-Manifolds
• Gravitational instantons of constant curvature
• All flat manifolds are cusps of hyperbolic orbifolds