Related papers: Jumps of the eta invariant
This article is a follow up of the previous article of the authors on the analytic surgery of eta- and rho-invariants. We investigate in detail the (Atiyah-Patodi-Singer)-rho-invariant for manifolds with boundary. First we generalize the…
For a closed, oriented, odd dimensional manifold $X$, we define the rho invariant $\rho(X,E,H)$ for the twisted odd signature operator valued in a flat hermitian vector bundle $E$, where $H = \sum i^{j+1} H_{2j+1}$ is an odd-degree closed…
We establish a formula for the spectral flow of a smooth family of twisted Dirac operators on a closed odd-dimensional Riemannian spin manifold, generalizing a result by Getzler. The spectral flow is expressed in terms of the $\hat{A}$-form…
The rho-invariant is an invariant of odd-dimensional manifolds with finite fundamental group, and lies in the representations modulo the regular representations (after tensoring with Q). It is a fundamental invariant that occurs in…
In previous work, we introduced eta invariants for even dimensional manifolds. It plays the same role as the eta invariant of Atiyah-Patodi-Singer, which is for odd dimensional manifolds. It is associated to $K^1$ representatives on even…
We study noncommutative eta- and rho-forms for homotopy equivalences. We prove a product formula for them and show that the rho-forms are well-defined on the structure set. We also define an index theoretic map from L-theory to C*-algebraic…
In previous work, we introduced eta invariants for even dimensional manifolds. It plays the same role as the eta invariant of Atiyah-Patodi-Singer, which is for odd dimensional manifolds. It is associated to $K^1$ representatives on even…
Relations between the Atiyah-Patodi-Singer rho invariant and signatures of links have been known for a long time, but they were only partially investigated. In order to explore them further, we develop a versatile cut-and-paste formula for…
We deduce an index jump formula for first order elliptic complexes over end-periodic manifolds, which generalizes the corresponding result for the DeRham complex. In the case of the anti-self-dual DeRham complex, we define the periodic rho…
On complete non-compact manifolds with bounded sectional curvature, we consider a class of self-adjoint Dirac-type operators called Dirac-Schr\"odinger operators. Assuming two Dirac-Schr\"odinger operators coincide at infinity, by previous…
This paper describes a topological method to compute the spectral flow of a family of twisted Dirac operators, it includes two detailed examples. Briefly, a formula of Atiyah, Patodi and Singer expresses the spectral flow in terms of…
We establish existence of the eta-invariant as well as of the Atiyah-Patodi-Singer and the Cheeger-Gromov rho-invariants for a class of Dirac operators on an incomplete edge space. Our analysis applies in particular to the signature, the…
Several proofs have been published of the Mod Z gluing formula for the eta-invariant of a Dirac operator. However, so far the integer contribution to the gluing formula for the eta-invariant is left obscure in the literature. In this…
This paper deals with the representations of the fundamental groups of compact surfaces with boundary into classical simple Lie groups of Hermitian type. We relate work on the signature of the associated local systems of…
This is a short version of math.DG/0505537. For an acyclic representation of the fundamental group of a compact oriented odd-dimensional manifold, which is close enough to a unitary representation, we define a refinement of the Ray-Singer…
Using H. Donnelly result from the article "Eta Invariants for G-Spaces" we calculate the eta invariants of the signature operator for almost all 7-dimensional flat manifolds with cyclic holonomy group. In all cases this eta invariants are…
We show that the R/Z part of the analytically defined eta invariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a…
We study analytic torsion and eta like invariants on CR contact manifolds of any dimension admitting a circle transverse action, and equipped with a unitary representation. We show that, when defined using the spectrum of relevant operators…
In 2005 a new topological invariant defined in terms of the Brouwer degree of a determinant map, was introduced by Musso, Pejsachowicz and the first name author for counting the conjugate points along a semi-Riemannian geodesic. This…
In this paper, we introduce an algebraic-topological invariant for commutative pm-rings, termed the spectral fundamental group, which is denoted by $\pi_{k}^{alg}(A)$. This group is defined via homotopy classes of loops within the space of…