The \(\eta\) invariant of the Atiyah-Patodi-Singer operator on compact flat manifolds

DOI10.1007/s10455-011-9307-8zbMath1268.58022OpenAlexW1972564596MaRDI QIDQ1759653

Ricardo A. Podestá, Roberto J. Miatello

Publication date: 21 November 2012

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10455-011-9307-8

zbMATH Keywords

flat manifoldssignature operator\(\eta\)-invariantcusp-cross-section

Mathematics Subject Classification ID

Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Other geometric groups, including crystallographic groups (20H15) Eta-invariants, Chern-Simons invariants (58J28) Other types of cobordism (57R90) Isospectrality (58J53)

Related Items (1)

The eta function and eta invariant of \(\mathbb{Z}_{2^r}\)-manifolds

Cites Work

• Unnamed Item
• Eta invariants for flat manifolds
• Eta invariants and class numbers
• The \(\eta\)-invariant of hyperbolic 3-manifolds
• Bieberbach groups and flat manifolds
• All flat three-manifolds appear as cusps of hyperbolic four-manifolds
• The computation of \(\eta\)-invariants on manifolds with free circle action
• On the geometric boundaries of hyperbolic 4-manifolds
• On the eta-invariant of some hyperbolic 3-manifolds
• Spectral theory of the Atiyah-Patodi-Singer operator on compact flat manifolds
• The eta invariant and equivariant bordism of flat manifolds with cyclic holonomy group of odd prime order
• Compact flat Riemannian manifolds. I
• Problems on Bieberbach groups and flat manifolds
• Integral Representations of Cyclic Groups of Prime Order
• Spectral asymmetry and Riemannian Geometry. I
• Spectral asymmetry and Riemannian geometry. II
• Spectral asymmetry and Riemannian geometry. III
• Geometric Invariants for Seifert Fibred 3-Manifolds
• Theη-Invariants of Cusped Hyperbolic 3-Manifolds
• The spectrum of twisted Dirac operators on compact flat manifolds
• The \(\eta\)-invariant of twisted Dirac operators of \(S^3/\Gamma\)
• Constructing hyperbolic manifolds which bound geometrically

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