$L^2$ -eta-invariants and their approximation by unitary eta-invariants
نویسندگان
چکیده
منابع مشابه
L–eta–invariants and Their Approximation by Unitary Eta–invariants
Cochran, Orr and Teichner introduced L–eta–invariants to detect highly non–trivial examples of non slice knots. Using a recent theorem by Lück and Schick we show that their metabelian L–eta–invariants can be viewed as the limit of finite dimensional unitary representations. We recall a ribbon obstruction theorem proved by the author using finite dimensional unitary eta–invariants. We show that ...
متن کاملEtale Groupoids, Eta Invariants and Index Theory
Let Γ be a discrete finitely generated group. Let M̂ → T be a Γ-equivariant fibration, with fibers diffeomorphic to a fixed even dimensional manifold with boundary Z. We assume that Γ → M̂ → M̂/Γ is a Galois covering of a compact manifold with boundary. Let (D(θ))θ∈T be a Γ-equivariant family of Dirac-type operators. Under the assumption that the boundary family is L-invertible , we define an inde...
متن کامل2 Eta Invariants of Homogeneous Spaces
We derive a formula for the η-invariants of equivariant Dirac operators on quotients of compact Lie groups, and for their infinitesimally equivariant extension. As an example, we give some computations for spheres. Quotients M = G/H of compact Lie groups form a very special class of manifolds, but yet they provide many important examples of Riemannian manifolds with non-negative sectional curva...
متن کاملEta Invariants as Sliceness Obstructions and Their Relation to Casson-gordon Invariants
We give a useful classification of the metabelian unitary representations of π1(MK), where MK is the result of zero-surgery along a knot K ⊂ S . We show that certain eta invariants associated to metabelian representations π1(MK)→ U(k) vanish for slice knots and that even more eta invariants vanish for ribbon knots and doubly slice knots. We show that our vanishing results contain the Casson–Gor...
متن کاملLink Concordance, Boundary Link Concordance and Eta-invariants
We study the eta-invariants of links and show that in many cases they form link concordance invariants, in particular that many eta-invariants vanish for slice links. This result contains and generalizes previous invariants by Smolinsky and Cha–Ko. We give a formula for the eta-invariant for boundary links. In several intersting cases this allows us to show that a given link is not slice. We sh...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2005
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004104008084