Related papers: Coronas and Callias type operators in coarse geome…

We present the properties of new Dirac-type operators generated by real or complex-valued special Killing-Yano tensors that are covariantly constant and represent roots of the metric tensor. In the real case these are just the so called…

We study a natural Dirac operator on a Lagrangian submanifold of a K\"ahler manifold. We first show that its square coincides with the Hodge-de Rham Laplacian provided the complex structure identifies the Spin structures of the tangent and…

An action of a torus T on a manifold M is locally standard if, at each point, the stabilizer is a sub-torus and the non-zero isotropy weights are a basis to its weight lattice. The quotient M/T is then a manifold-with-corners, decorated by…

In this note, we prove lower and upper bounds for Dirac operators of submanifolds in certain ambient manifolds in terms of conformal and extrinsic quantities.

We give a derivation of the Dirac operator on the noncommutative $2$-sphere within the framework of the bosonic fuzzy sphere and define Connes' triple. It turns out that there are two different types of spectra of the Dirac operator and…

We prove cobordism index invariance for pseudo-differential elliptic operators on closed orbifolds with $K$--theoretical methods.

Dirac operators and Dirac cohomology for Lie superalgebras of Riemannian type, introduced by Huang and Pand\v{z}i\'{c}, provide an effective tool for the study of unitarizable supermodules. In this article, we study these objects for Lie…

We pursue an old conjecture of John Roe about the algebraic K-theory of the algebra of finite propagation, locally trace-class operators, namely that transgressing the algebraic coarse character map on this algebra to a Higson dominated…

We investigate the evaluation of the Dirac index using symplectic geometry in the loop space of the corresponding supersymmetric quantum mechanical model. In particular, we find that if we impose a simple first class constraint, we can…

This current article aims to study a new subclass of meromorphic functions with positive coefficients by reconstructing a new operator in the punctured open disc. Also, some geometric properties are considered and investigated, such results…

Suppose that an algebraic torus $G$ acts algebraically on a projective manifold $X$ with generically trivial stabilizers. Then the Zariski closure of the set of pairs $\{(x,y)\in X\times X\mid y=gx \text{for some}g\in G\}$ defines a nonzero…

We provide a comprehensive lattice formulation of various types of the Dirac operator indices, employing $K$-theory to classify the Wilson Dirac operator via its spectral flow. In contrast to the index of the overlap Dirac operator defined…

We present a version of the Penrose transform which relates compactly supported cohomology on a complex or CR manifold Z to kernels and cokernels of differential operators on a parameter space X of compact complex submanifolds of Z.

Let G be a compact connected semisimple Lie group and let H\subset G be a closed connected subgroup such that rank(G)=rank(H) and G/H is a symmetric space. Given an irreducible representation of H, we define a Dirac operator D and determine…

There are a number of (co-)homology theories on coarse spaces. Controlled operator K-theory is by far the most popular one of them. Our approach is geometric. We study when does the Roe-algebra of a space restrict to a subspace. Then we…

For a Dirac operator $D_{\bar{g}}$ over a spin compact Riemannian manifold with boundary $(\bar{X},\bar{g})$, we give a natural construction of the Calder\'on projector and of the associated Bergman projector on the space of harmonic…

A differential operator $D$ commuting with an $S^1$-action is said to be rigid if the non-constant Fourier coefficients of $\ker D$ and $\coker D$ are the same. Somewhat surprisingly, the study of rigid differential operators turns out to…

We construct a corank one Poisson manifold which is of strong compact type, i.e., the associated Lie algebroid structure on its cotangent bundle is integrable, annd the source 1-conected (symplectic) integration is compact. The construction…

We give a local formula for the index of a transverse Dirac-type operator on a compact manifold with a Riemannian foliation, under the assumption that the Molino sheaf is a sheaf of abelian Lie algebras.

It is shown that the second order symmetry operators for the Dirac equation on a general two-dimensional spin manifold may be expressed in terms of Killing vectors and valence two Killing tensors. The role of these operators in the theory…