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.
Proves almost flat spin^c manifolds bound compact manifolds.
Proves functoriality in geometric quantization for non-compact spin-c manifolds.
New rigidity theorems for spin^c manifolds using modular invariance.
No Hantzsche-Wendt manifolds over 3D admit spin^c structures.
In this paper, we extend the study of generalized Killing spinors on Riemannian Spin manifolds started by Moroianu and Herzlich to complex Killing functions. We prove that such spinor fields are always real Spin Killing spinors or imaginary generalized Spin Killing spinors, providing that the dimension of t…
Classifies manifolds with specific spinors and constructs parallel spinors.
Totally umbilical hypersurfaces in Spin^c manifolds with special spinors have constant mean curvature.
Simplified proof of spin^c structures using twistor spaces.
We derive various pinching results for small Dirac eigenvalues using the classification of and spin manifolds admitting nontrivial Killing spinors. For this, we introduce a notion of convergence for manifolds which involves a general study on convergence of Riemannian manifolds with a pr…
A G-equivariant spin^c structure on a manifold gives rise to a virtual representation of the group G, called the spin^c quantization of the manifold. We present a cutting construction for S^1-equivariant spin^c manifolds, and show that the quantization of the original manifold is isomorphic to the direct sum of the qua…
Study shows rigidity for spin^c manifolds with foliated boundaries.
Odd-dimensional Riemannian manifolds admit pure spin-c Killing spinors if and only if they are α-Sasakian.
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…
The paper classifies hypersurfaces in Spin manifolds that satisfy a specific inequality.
The study finds hyperbolic manifolds without spin^c structures in dimensions 5 and above.
We define spin-c prequantization of a symplectic manifold to be a spin-c structure and a connection which are compatible with the symplectic form. We describe the cutting of an S^1-equivariant spin-c prequantization. The cutting process involves a choice of a spin-c prequantization for the complex plane. We prove that …
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…
We characterize certain CR structures of arbitrary codimension (different from 3, 4 and 5) on Riemannian Spin manifolds by the existence of a Spin structure carrying a strictly partially pure spinor field. Furthermore, we study the geometry of Riemannian Spin manifolds carrying a strictly partially pure spi…
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 define a `Higgs field' for a four-dimensional spin-manifold to be a smooth section of its positive half-spinor bundle, transverse to the zero section, and defined only up to a positive functional factor. This is intended to be a generalization of almost complex structures on real four-manifolds, each of which ma…
We show that a homotopy equivalence between manifolds induces a correspondence between their spin^c-structures, even in the presence of 2-torsion. This is proved by generalizing spin^c-structures to Poincare complexes. A procedure is given for explicitly computing the correspondence under reasonable hypotheses.
The Seiberg-Witten equations are lifted to Kaluza-Klein 5-manifolds.
The study explores psc-metrics on non-spin manifolds with pin^\pm or spin^c structures.
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 …
It is well known that spinors on oriented Riemannian manifolds cannot be defined as sections of a vector bundle associated with the frame bundle. For this reason spin and spin^c structures are often introduced. In this paper we prove that spin^c structures have a universal property among all other structures that enabl…
By studying modular invariance properties of some characteristic forms, we obtain twisted anomaly cancellation formulas. We apply these twisted cancellation formulas to study divisibilities on spin manifolds and congruences on spin manifolds. Especially, we get twisted Rokhlin congruences for dimensional spi…
New spinor fields reveal local or global geometric properties of manifolds.
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.
Quantum invariant constructed for sutured 3-manifolds using Hopf superalgebra.
Simply connected 3-dimensional homogeneous manifolds , with 4-dimensional isometry group, have a canonical Spin structure carrying parallel or Killing spinors. The restriction to any hypersurface of these parallel or Killing spinors allows to characterize isometric immersions of surfaces into . As…
The study classifies spin manifolds with positive generalized scalar curvature.
Develops spinorial description of CR structures of arbitrary codimension.
This paper gives a combinatorial description of spin and spin^c-structures on triangulated PL-manifolds of arbitrary dimension. These formulations of spin and spin^c-structures are established primarily for the purpose of aiding in computations. The novelty of the approach is we rely heavily on the naturality of binary…
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…
Study proves Witten genera vanish for certain manifolds, supporting a conjecture.
We present a definition of Riemannian manifold in noncommutative geometry. Using products of unbounded Kasparov modules, we show one can obtain such Riemannian manifolds from noncommutative spin^c manifolds; and conversely, in the presence of a spin^c structure. We also show how to obtain an analogue of Kasparov's fund…
New formulas derived from modular forms for manifold indices.
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…
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…
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.
This paper explores conditions for positive scalar curvature on spin^c manifolds.
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…
Sharp inequalities for Kähler manifolds' systolic invariants are established.
Eta invariant computed for circle bundles over Fano manifolds.
We construct a generalized Witten genus for spin manifolds, which takes values in level 1 modular forms with integral Fourier expansion on a class of spin manifolds called string manifolds. We also construct a mod 2 analogue of the Witten genus for dimensional spin manifolds. The Landweber-Stong type…
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…
New real invariants for 3-manifolds and links.
Alternative proof and description of orientations for instanton moduli spaces.