Related papers: Eta invariants for flat manifolds
Integral invariants obtained from Principal Component Analysis on a small kernel domain of a submanifold encode important geometric information classically defined in differential-geometric terms. We generalize to hypersurfaces in any…
In this note we show that every integer is the signature of a non-compact, oriented, hyperbolic 4-manifold of finite volume, and give some partial results on the geography of such manifolds. The main ingredients are a theorem of Long and…
We study fixed point sets for holomorphic automorphisms (and endomorphisms) on complex manifolds. The main object of our interest is to determine the number and configuration of fixed points that forces an automorphism (endomorphism) to be…
The exceptional holonomy groups are G2 in 7 dimensions, and Spin(7) in 8 dimensions. Riemannian manifolds with these holonomy groups are Ricci-flat. This is a survey paper on constructions for compact 7- and 8-manifolds with holonomy G2 and…
Any smooth, closed oriented 4-manifold has a surface diagram of arbitrarily high genus g>2 that specifies it up to diffeomorphism. The goal of this paper is to prove the following statement: For any smooth, closed oriented 4-manifold M,…
This paper demonstrates the power of the calculus developed in the two previous parts of the series for all real forms of the almost Hermitian symmetric structures on smooth manifolds, including e.g. conformal Riemannian and almost…
In this note, we prove the regularity of eta forms by the Clifford asymptotics. Then we generalize this result to the equivariant case.
We study the index of the APS boundary value problem for a strongly Callias-type operator $D$ on a complete even dimensional Riemannian manifold $M$ (the odd dimensional case was considered in our previous paper arXiv:1706.06737). We use…
Let $(M, \omega)$ be a connected, compact 6-dimensional symplectic manifold equipped with a semi-free Hamiltonian $S^1$ action such that the fixed point set consists of isolated points or surfaces. Assume dim $H^2(M)<3$, in \cite{L}, we…
In this note, we find the conditions on an odd-dimensional Riemannian manifolds under which its twistor space is eta-Einstein.
We study the special algebraic properties of alternating 3-forms in 6 and 7 dimensions and introduce a diffeomorphism-invariant functional on the space of differential 3-forms on a closed manifold M in these dimensions. Restricting the…
This is a note for the conference proceedings Topological and Geometrical Problems related to Quantum Field Theory. We summarize our joint work with Dai about eta invariants on manifolds with boundary. Then we apply these results to prove…
We calculate the Chern-Simons invariants of the twist knot orbifolds using the Schl\"{a}fli formula for the generalized Chern-Simons function on the family of the twist knot cone-manifold structures. Following the general instruction of…
The topological significance of the spectral Atiyah-Patodi-Singer eta-invariant is investigated under the parity conditions of P. Gilkey. We show that twice the fractional part of the invariant is computed by the linking pairing in K-theory…
In this paper we give a new proof of Bismut-Freed's result on the local regularity of the eta invariant of a Dirac operator in odd dimension.
We give a necessary and suffcient condition for almost-flat manifolds with cyclic holonomy to admit a Spin structure. Using this condition we find all 4-dimensional orientable almost- flat manifolds with cyclic holonomy that do not admit a…
The results of this paper have been subsumed by the paper "A geometric invariant theory construction of spaces of stable maps," Elizabeth Baldwin and David Swinarski, arXiv:0706.1381
We define a renormalized characteristic class for Einstein asymptotically complex hyperbolic (ACHE) manifolds of dimension 4: for any such manifold, the polynomial in the curvature associated to the characteristic class euler-3signature is…
We describe the topology of the moduli spaces of flat metrics for all the 3-dimensional closed manifolds. We give an algebraic description of the moduli spaces for the 4-dimensional closed flat manifolds with a single generator in their…
We prove two geometric index theorems for a family of first-order elliptic operators over a manifold with boundary by computing eta form representatives for the Chern character classes of the index bundle. The eta forms occur as relative…