arXiv research

In this paper, we prove an equivariant Kastler-Kalau-Walze type theorem for spin manifolds without boundary. For $6$ dimensional spin manifolds with boundary, we also give an equivariant Kastler-Kalau-Walze type theorem. Then we generalize this theorem to the general $n$ dimensional manifold. An equivariant Kastler-Kal…

Proves Kastler-Kalau-Walze theorem for spectral Einstein functional on low-dimensional manifolds.

Generalizes Kastler-Kalau-Walze theorem to even-dimensional manifolds.

Study perturbs Dirac operator on 4D manifolds, proving Kastler-Kalau-Walze theorems.

The paper proves two theorems for modified Novikov operators under conformal perturbations.

Develops a theorem for a 6D manifold with boundary.

The paper proves new theorems for Dirac operators on even-dimensional manifolds with boundary.

Defines and proves generalized noncommutative residue theorems for specific dimensions.

In this paper, we establish some general Kastler-Kalau-Walze type theorems for any dimensional manifolds with boundary which generalize the results in [WW1].

The paper calculates transformation operators and proves a theorem on 4D manifolds.

The paper proves formulas and theorems for J-Witten deformation on specific manifolds.

The paper proves formulas and theorems for sub-signature operators on manifolds with or without boundaries.

The paper proves formulas and theorems for statistical de Rham Hodge operators on manifolds with boundary.

The paper proves formulas and theorems for Dirac-Witten operators on manifolds with or without boundaries.

Defines and computes a generalized spectral action for Lorentz warped products.

The paper proves a theorem for a twisted Dirac operator on specific manifolds.

The paper proves a theorem for a twisted Dirac operator on specific manifolds.

The paper proves formulas and theorems for specific operators on manifolds.

Paper derives sub-Riemannian versions of Kastler-Kalau-Walze and Dabrowski-Sitarz-Zalecki theorems for twisted BCV spaces.

In this paper, we give a brute-force proof of the Kastler-Kalau-Walze type theorem for $7$-dimensional manifolds with boundary about Witten deformation, and give a theoritic explaination of the gravitational action for $7$ dimensional manifolds with boundary.

The paper studies perturbations of de Rham Hodge operators on manifolds with or without boundaries.

In this paper, we define lower dimensional volumes of spin manifolds with boundary. We compute the lower dimensional volume ${\rm Vol}^{(2,2)}$ for 5-dimensional and 6-dimensional spin manifolds with boundary and we also get the Kastler-Kalau-Walze type theorem in this case.

Proves two theorems on odd-dimensional manifolds with boundary.

Defines spectral Einstein functional for manifolds with boundary.

The paper proves new theorems about specific types of operator perturbations.

In this paper, we prove a Kastler-Kalau-Walze type theorem for perturbations of Dirac operators on compact manifolds with or without boundary. As a corollary, we give two kinds of operator-theoretic explanations of the gravitational action on boundary. We also compute the spectral action for Dirac operators with two-fo…

In this paper, we define lower dimensional volumes of spin manifolds with boundary. We compute the lower dimensional volume ${\rm Vol}_{6}^{(1,3)}$ for 6-dimensional spin manifolds with boundary and the gravity on boundary is derived by the noncommutative residue associated with Dirac operators.For 6-dimensional manifo…

The paper computes a residue density for a specific Laplacian on compact manifolds.

Extends Einstein-Hilbert action to higher-order spectral triples.

The paper calculates the noncommutative residue for a rescaled Dirac operator on 6D manifolds.

In this paper, we compute the adiabatic limit of the scalar curvature and prove several vanishing theorems, we also derive a Kastler-Kalau-Walze type theorem for the noncommutative residue in the case of foliations.

In this paper, we establish two kinds of Kastler-Kalau-Walze type theorems for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection on six-dimensional manifolds with boundary.

In this paper, we define lower dimensional volumes of compact Riemannian manifolds with boundary. For five dimensional spin manifolds with boundary, we prove a Kastler-Kalau-Walze type theorem associated with one-form perturbations of Dirac operators in this case.

In this paper, we get a Kastler-Kalau-Walze type theorem associated to nonminimal de Rham-Hodge operators on compact manifolds with boundary. We give two kinds of operator-theoretic explanations of the gravitational action in the case of four dimensional compact manifolds with flat boundary.

We prove a Kastler-Kalau-Walze type theorem for the Dirac operator and the signature operator for $3,4$-dimensional manifolds with boundary. As a corollary, we give two kinds of operator theoretic explanations of the gravitational action in the case of 4-dimensional manifolds with flat boundary.

In this paper, we give two Lichnerowicz type formulas for modified Novikov operators. We prove KastlerKalau-Walze type theorems for modified Novikov operators on compact manifolds with (resp.without) boundary. We also compute the spectral action for Witten deformation on 4-dimensional compact manifolds.

In this paper, we give two Lichnerowicz type formulas for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection. We also prove two Kastler-Kalau-Walze type theorems for twisted Dirac operators and twisted signature operators on 4-dimensional manifolds with (resp. without) boun…

Proves K-K-W type theorems for specific types of operators.

In this paper, we define lower dimensional volumes associated to sub-Dirac operators for foliations. In some cases, we compute these lower dimensional volumes. We also prove the Kastler-Kalau-Walze type theorems for foliations with or without boundary. As a corollary, we give an explanation of the gravitational action …

In this paper, we prove a Kastler-Kalau-Walze type theorem for 4-dimensional and 6-dimensional spin manifolds with boundary associated with the conformal Robertson-Walker metric. And we give two kinds of operator theoretic explanations of the gravitational action for boundary in the case of 4-dimensional manifolds with…