arXiv research

The paper derives statistics of multi-factor functions from their Fourier transforms.

The extremely useful method of Malliavin calculus has not yet gained adequate popularity because of the complicated analytic apparatus of this method. The author attempts here to propose a simplified algebraic formalism similar to Malliavin calculus, but based on the notion of creation-annihilation operators instead of…

We prove that if Q is a finite quasigroup quandle, then |Q| annihilates the torsion of its homology. It is a classical result in reduced homology of finite groups that the order of a group annihilates its homology. From the very beginning of the rack homology (between 1990 and 1995) the analogous result was suspected. …

It is a classical result in reduced homology of finite groups that the order of a group annihilates its homology. Similarly, we have proved that the torsion subgroup of rack and quandle homology of a finite quasigroup quandle is annihilated by its order. However, it does not hold for connected quandles in general. In t…

The paper describes a new geometric structure for general Clifford algebras.

A theorem proves integrability of Fréchet tangent distributions.

Study eigenvalues of curvature operators to annihilate cobordism invariants.

The paper studies the center of the Goldman Lie algebra and its properties.

Study on symmetric operators on non-compact manifolds, focusing on their index modulo 2.

The Dirac operator d+delta on the Hodge complex of a Riemannian manifold is regarded as an annihilation operator A. On a weighted space L_mu^2 Omega, [A,A*] acts as multiplication by a positive constant on excited states if and only if the logarithm of the measure density of mu satisfies a pair of equations. The equati…

Proves a lattice version of the Atiyah-Singer index theorem.

Formulates Index III lemma and Rauch III theorem with applications.

The paper derives a formula for Lefschetz number of a geometric endomorphism.

Explain Arnold's proof of the Morse index theorem using Maslov index.

The paper studies polynomials and ideals from colored Jones polynomials for links.

We give a short proof of the Morse index theorem for geodesics in semi-Riemannian manifolds by using K-theory. This makes the Morse index theorem reminiscent of the Atiyah-Singer index theorem for families of selfadjoint elliptic operators.

Researchers prove an equivariant index theorem on Euclidean space.

In this note, we show that the obstruction classes of deforming vector forms on a compact Kähler manifold is annihilated by cohomology classes.

Extends a theorem for first-order elliptic operators on manifolds.

Let $M$ be a closed connected smooth manifold and $G=\textmd{Diff}_0(M)$ denote the connected component of the diffeomorphism group of $M$ containing the identity. The natural action of $G$ on $M$ induces the trace homomorphism on homology. We show that the image of trace homomorphism is annihilated by the subalgebra o…

The paper proves an index theorem for loop spaces of compact manifolds.

In this paper, we prove a local equivariant index theorem for sub-signature operators which generalizes the Zhang's index theorem for sub-signature operators.

Proves an equivariant version of index theorem for geometric families.

We prove an index theorem for families of linear periodic Hamiltonian systems, which is reminiscent of the Atiyah-Singer index theorem for selfadjoint elliptic operators. For the special case of one-parameter families, we compare our theorem with a classical result of Salamon and Zehnder. Finally, we use the index theo…

We establish a mod 2 index theorem for real vector bundles over 8k+2 dimensional compact pin$^-$ manifolds. The analytic index is the reduced $η$ invariant of (twisted) Dirac operators and the topological index is defined through $KO$-theory. Our main result extends the mod 2 index theorem of Atiyan and Singer to non-o…

Extends index theorem to domain walls with discontinuous Riemannian connections.

In this note, we prove an index theorem on Galois covering for Heisenberg elliptic differential operators, which is not elliptic, analogous to Atiyah's $Γ$-index theorem. This note also contains an example of Heisenberg differential operators with non-trivial $Γ$-index.

Atiyah-Singer theorem links math fields, predicts topological insights.

Massive fermions help understand index theorems without chiral symmetry.

Abstract: Review of Index theorem and its applications.

A recent anomaly computation of Horava and Witten is proved and generalized in the form of two index theorems in odd dimensions. Theorem A is a fixed point formula for orientation-reversing involutions. Theorem B is an index theorem for manifolds with boundary using local boundary conditions. Both hold for families of …

Proves Morse index theorem for geodesics in conic Finsler manifolds.

Paper introduces Lie algebroid index theory and a generalized Riemann-Roch theorem.

The paper proves index theorems for graph-based optimal control problems.

Absolute index theorem for warped product manifolds.

Paper provides a rigorous proof of the index theorem for economists.

In this paper, we prove a Morse index theorem for the index form of regular Lagrangian system with selfadjoint boundary condition.

In this paper, we extend Roe's cyclic $1$-cocycle to relative settings. We also prove two relative index theorems for partitioned manifolds by using its cyclic cocycle, which are generalizations of index theorems on partitioned manifolds. One of these theorems is a variant of [M. Karami-A.H.S. Sadegh-M.E. Zadeh, arXiv:…

In this talk, we review the heat kernel approach to the Atiyah-Singer index theorem for Dirac operators on closed manifolds, as well as the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary. We also discuss the odd dimensional counterparts of the above results. In particular, we describe…

In his book (II.5), Connes gives a proof of the Atiyah-Singer index theorem for closed manifolds by using deformation groupoids and appropiate actions of these on R^N. Following these ideas, we prove an index theorem for manifolds with boundary.

In this paper we show an index theorem for gerbes

Higher index theorem for Dirac operators on finite-volume spaces.

Researchers construct an index map for contact manifolds using K-theory.

An expression is found for the $L^2$-index of a Dirac operator coupled to a connection on a $U_n$ vector bundle over $S^1\times{\mathbb R}^3$. Boundary conditions for the connection are given which ensure the coupled Dirac operator is Fredholm. Callias' index theorem is used to calculate the index when the connection i…

We give a superconnection proof of Connes' index theorem for proper cocompact actions of etale groupoids. This includes Connes' general foliation index theorem for foliations with Hausdorff holonomy groupoid.

Formulas for spectra of higher spin operators on sphere subbundles.

In [Wu], the noncommutative Atiyah-Patodi-Singer index theorem was proved. In this paper, we extend this theorem to the equivariant case.

Proves a theorem for mechanical systems with reflections.