A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New rigidity theorems for spin^c manifolds using modular invariance.
An integer valued topological index of a Dirac operator is introduced for a pair of a 4n+2 dimensional open Spin^c manifold and a section of the determinant line bundle satisfying some property. We show a relation between the index and an index of a Dirac operator of its characteristic submanifold, by a localization of…
In this paper, we extend the Hijazi inequality, involving the Energy-Momentum tensor, for the eigenvalues of the Dirac operator on manifolds without boundary. The limiting case is then studied and an example is given.
We define an equivariant index of Spin-Dirac operators on possibly noncompact manifolds, acted on by compact, connected Lie groups. The main result in this paper is that the index decomposes into irreducible representations according to the quantisation commutes with reduction principle.
In this paper, we give a geometric expression for the multiplicities of the equivariant index of a spin-c Dirac operator.
The paper describes spectra of operators on rational homogeneous varieties.
We study boundary value problems for the Dirac operator on Riemannian Spin manifolds of bounded geometry and with noncompact boundary. This generalizes a part of the theory of boundary value problems by C. Bär and W. Ballmann for complete manifolds with closed boundary. As an application, we derive the lower bound …
We establish a lower bound for the eigenvalues of the Dirac operator defined on a compact Kähler-Einstein manifold of positive scalar curvature and endowed with particular structures. The limiting case is characterized by the existence of Kählerian Killing spinors in a certain subbundle of…
The study explores psc-metrics on non-spin manifolds with pin^\pm or spin^c structures.
We derive an inequality that relates nodal set and eigenvalues of a class of twisted Dirac operators on closed surfaces and point out how this inequality naturally arises as an eigenvalue estimate for the Dirac operator. This allows us to obtain eigenvalue estimates for the twisted Dirac operator appearing…
New formulas derived from modular forms for manifold indices.
Eta invariant computed for circle bundles over Fano manifolds.
Sharp inequality for complex projective space's systoles under scalar curvature bounds.
We extend to the eigenvalues of the hypersurface Spin Dirac operator well known lower and upper bounds. Examples of limiting cases are then given. Futhermore, we prove a correspondence between the existence of a Spin Killing spinor on homogeneous 3-dimensional manifolds with 4-dimensional is…
We establish the existence of the asymptotic expansion of the Bergman kernel associated to the spin-c Dirac operators acting on high tensor powers of line bundles with non-degenerate mixed curvature (negative and positive eigenvalues) by extending the paper " On the asymptotic expansion of Bergman kernel " (math.DG/040…
Alternative proof and description of orientations for instanton moduli spaces.
In this paper, we estimate the eigenvalues of the twisted Dirac operator on Kähler submanifolds of the complex projective space and we discuss the sharpness of this estimate for the embedding .
We establish a vanishing result for indices of certain twisted Dirac operators on -manifolds with non-abelian Lie-group actions. We apply this result to study non-abelian symmetries of quasitoric manifolds. We give upper bounds for the degree of symmetry of these manifolds.
Revisits zero modes of Dirac operator on Eguchi-Hanson space.
We study the asymptotic of the spectrum of the \spin Dirac operator on high tensor powers of a line bundle. As application, we get a simple proof of the main result of Guillemin-Uribe, which was originally proved by using the analysis of Toeplitz operators of Boutet de Monvel and Guillemin.
We establish the factorization of Dirac operators on Riemannian submersions of compact spin manifolds in unbounded KK-theory. More precisely, we show that the Dirac operator on the total space of such a submersion is unitarily equivalent to the tensor sum of a family of Dirac operators with the Dirac operator on th…
The Dirac operator for a manifold Q, and its chirality operator when Q is even dimensional, have a central role in noncommutative geometry. We systematically develop the theory of this operator when Q=G/H, where G and H are compact connected Lie groups and G is simple. An elementary discussion of the differential geome…
In this paper, we first establish an -equivariant index theorem for Spin Dirac operators on manifolds, then combining with the methods developed by Taubes \cite{MR998662} and Liu-Ma-Zhang \cite{MR1870666,MR2016198}, we extend Witten's rigidity theorem to the case of Spin manif…
We study the asymptotic of the Bergman kernel of the spin Dirac operator on high tensor powers of a line bundle.
On manifolds, we study the Energy-Momentum tensor associated with a spinor field. First, we give a spinorial Gauss type formula for oriented hypersurfaces of a manifold. Using the notion of generalized cylinders, we derive the variationnal formula for the Dirac operator under metric deformation and po…
We compute the second coefficient of the composition of two Berezin-Toeplitz operators associated with the Dirac operator on a symplectic manifold, making use of the full-off diagonal expansion of the Bergman kernel.
In this paper, we write down Seiberg-Witten equations on contact metric manifolds of dimension 5. Any contact metric manifold has a spin^c structure. For Dirac equation we use Dirac type operators associated to the generalized Tanaka-Webster connection on spin^c spinor bundle of a contact metric manifold. For curvature…
Let be a compact connected Lie group, and a compact Hamiltonian -space, with moment map . For each -equivariant Hermitian vector bundle over , one has an associated twisted Spin-C Dirac operator, whose equivariant index is a symplectic invariant of . In the present paper, we study gluing prop…
In this paper, we extend the Hijazi type inequality, involving the Energy-Momentum tensor, to the eigenvalues of the Dirac operator on complete Riemannian Spin manifolds without boundary and of finite volume. Under some additional assumptions, using the refined Kato inequality, we prove the Hijazi type inequality f…
The paper classifies hypersurfaces in Spin manifolds that satisfy a specific inequality.
Classifies manifolds with specific spinors and constructs parallel spinors.
We study two quantization schemes for compact symplectic manifolds with almost complex structures. The first of these is the Spin-c quantization. We prove the analog of Kodaira vanishing for the Spin-c Dirac operator, which shows that the index space of this operator provides an honest (not virtual) vector space semicl…
Paper extends variational formula for Bismut-Cheeger eta form, proving key theorems in K-theory.
This paper explores conditions for positive scalar curvature on spin^c manifolds.
Paradan and Vergne generalised the quantisation commutes with reduction principle of Guillemin and Sternberg from symplectic to Spin-manifolds. We extend their result to noncompact groups and manifolds. This leads to a result for cocompact actions, and a result for non-cocompact actions for reduction at zero. The r…
Constructs small bundle gerbes and proves index theorems for manifolds.
We study two special cases of the equivariant index defined in part I of this series. We apply this index to deformations of Spin-Dirac operators, invariant under actions by possibly noncompact groups, with possibly noncompact orbit spaces. One special case is an index defined in terms of multiplicities of discrete…
We extend our earlier work in [TZ1], where an analytic approach to the Guillemin-Sternberg conjecture [GS] was developed, to cases where the Spin-complex under consideration is allowed to be further twisted by certain natural exterior power bundles. The main result is a weighted quantization formula in the presence…
We record an answer to the question "In which dimensions is the connected sum of two closed almost complex manifolds necessarily an almost complex manifold?". In the process of doing so, we are naturally led to ask "For which values of l is the connected sum of l closed almost complex manifolds necessarily an almost co…
We extend our earlier work in [TZ1], where an analytic approach to the Guillemin-Sternberg conjecture [GS] was developed, to cases where the Spin^c-complex under consideration is allowed to be further twisted by certain exterior power bundles of the cotangent bundle. The main result is a weighted quantization formula i…
The study classifies spin manifolds with positive generalized scalar curvature.
In this note, we look at estimates for the scalar curvature k of a Riemannian manifold M which are related to spin^c Dirac operators: We show that one may not enlarge a Kaehler metric with positive Ricci curvature without making k smaller somewhere on M. We also give explicit upper bounds for min(k) for arbitrary Riema…
Researchers compute Floer homotopy types and eta invariants for Seifert 3-manifolds.
We develop the theory of Berezin-Toeplitz operator on any compact symplectic prequantizable manifold from scratch. Our main inspiration is the Boutet de Monvel-Guillemin theory, that we simplify in several ways to obtain a concise exposition. A comparison with the spin-c Dirac quantization is also included.
Constructs differential models for twisted Spin^c-bordism and its dual, defining a new anomaly map.
In his book Mickelsson notices that the infinite-dimensional Grassmannian manifold of Segal and Wilson admits a Spin^c structure and after this he naturally considers the problem of defining a Dirac operator on it. Mickelsson gives a possible candidate for such an operator but unfortunately it proves out to be badly di…
We study general conditions under which the computations of the index of a perturbed Dirac operator localize to the singular set of the bundle endomorphism in the semi-classical limit . We show how to use Witten's method to compute the index of by doing a combinatorial computation inv…
Study Floer theory of hyperbolic three-manifolds using Dirac spectral flow.