arXiv research

The study introduces a new function to analyze special holonomy manifolds.

Holonomy perturbations affect character varieties of tangles, leading to smooth manifolds.

Study shows how tangle moduli spaces relate to boundary surfaces.

Dunfield-Garoufalidis and Boyer-Zhang proved that the A-polynomial of a nontrivial knot in $S^{3}$ is nontrivial. In this paper, we use holonomy perturbations to prove the non-triviality of the A-polynomial for a nontrivial, null-homotopic knot in an irreducible 3-manifold. Also, we give a strong constraint on the A-po…

Study character varieties of tangles to map immersed curves in the pillowcase.

Study linear perturbations of Spin(7) metrics, finding only rank one nilpotent matrices.

The article constructs an invariant for foliations without holonomy-invariant transverse measure.

Study knots with bounded $SU(2)$-cyclic slopes and unique limit point.

Integer homology 3-spheres have irreducible SU(2) representations.

Infinitely many M2-instantons affect M-theory on G2-manifolds.

Researchers find new $G_2$-conifolds in $M$-theory with potential field theory duals.

New proof for 3-manifolds with specific homology groups.

The Casson invariant is calculated for non-trivial bundles, influenced by cohomology ring properties.

Scheme for generating sets in knot homology for lens spaces.

The paper examines gravitational singularities in spacetimes and proves inextendibility.

We prove that the moduli space of solutions to the PU(2) monopole equations is a smooth manifold of the expected dimension for simple, generic parameters such as (and including) the Riemannian metric on the given four-manifold. In a previous article, dg-ga/9710032, we proved transversality using an extension of the hol…

A surgery on a knot in 3-sphere is called SU(2)-cyclic if it gives a manifold whose fundamental group has no non-cyclic SU(2) representations. Using holonomy perturbations on the Chern-Simons functional, we prove that the distance of two SU(2)-cyclic surgery coefficients is bounded by the sum of the absolute values of …

Two new proofs provide Eguchi-Hanson metrics as ALE bubbles for Kummer constructions of K3 metrics.

We prove that a given Calabi-Yau threefold with a stable holomorphic vector bundle can be perturbed to a solution of the Strominger system provided that the second Chern class of the vector bundle is equal to the second Chern class of the tangent bundle. If the Calabi-Yau threefold has strict SU(3) holonomy then the eq…

Proves SU(2) representations for certain 3-spheres with embedded tori.

We introduce explicit holonomy perturbations of the Chern-Simons functional on a 3-ball containing a pair of unknotted arcs. These perturbations give us a concrete local method for making the moduli spaces of flat singular SO(3) connections relevant to Kronheimer and Mrowka's singular instanton knot homology non-degene…

The expectation value of Wilson loop operators in three-dimensional SO(N) Chern-Simons gauge theory gives a known knot invariant: the Kauffman polynomial. Here this result is derived, at the first order, via a simple variational method. With the same procedure the skein relation for Sp(N) are also obtained. Jones polyn…

We study the differential geometry of principal G-bundles whose base space is the space of free paths (loops) on a manifold M. In particular we consider connections defined in terms of pairs (A,B), where A is a connection for a fixed principal bundle P(M,G) and B is a 2-form on M. The relevant curvatures, parallel tran…

Study on counting flat connections over $G_2$-orbifolds, proving moduli space compact and smooth.

This paper studies the relation between two notions of holonomy on a conformal manifold. The first is the conformal holonomy, defined to be the holonomy of the normal tractor connection. The second is the holonomy of the Fefferman-Graham ambient metric of the conformal manifold. It is shown that the infinitesimal confo…

In these notes, we carefully analyze the properties of the "ramified" Seiberg-Witten equations associated with supersymmetric configurations of the Seiberg-Witten abelian gauge theory with surface operators on an oriented closed four-manifold X. We find that in order to have sensible solutions to these equations, only …

The study of holonomy groups in flat solvmanifolds, proving finite abelian groups can be holonomy groups and describing dimensions.

We study a class of asymptotically cylindrical Ricci-flat Kähler metrics arising on quasiprojective manifolds. Using the Calabi--Yau geometry and analysis and the Kodaira--Kuranishi--Spencer theory and building up on results of N.Koiso for the case of compact manifolds, we show that under rather general hypotheses any …

Holonomy of Weyl connections in Lorentzian space classified.

New method for foliated bundles using holonomy groupoids.

Holonomy groups of metric connections converge in a monotonic way.

The problem of classification of connected holonomy groups (equivalently of holonomy algebras) for pseudo-Riemannian manifolds is open. The classification of Riemannian holonomy algebras is a classical result. The classification of Lorentzian holonomy algebras was obtained recently. In the present paper weakly-irreduci…

Defines equivariant holonomy for U(1)-bundles, generalizing properties.

Defines and analyzes the holonomy Lie algebra of geometric lattices.

Classifies holonomy groups for special geometric structures.

Classifies holonomy algebras of Lorentz-Kähler manifolds.

Holonomy groups and holonomy algebras for connections on locally free sheaves over supermanifolds are introduced. A one-to-one correspondence between parallel sections and holonomy-invariant vectors, and a one-to-one correspondence between parallel locally direct subsheaves and holonomy-invariant vector supersubspaces …

We study the normal holonomy group, i.e. the holonomy group of the normal connection, of a CR-submanifold of a complex space form. We complete the local classification of normal holonomies for complex submanifolds. We show that the normal holonomy group of a coisotropic submanifold acts as the holonomy representation o…

Proof that Ricci flow preserves full holonomy group.

Holonomy groups of K-contact sub-Riemannian manifolds are studied.

The problem of classification of connected holonomy groups (equivalently of holonomy algebras) for pseudo-Riemannian manifolds is open. The classification of Riemannian holonomy algebras is a classical result. The classification of Lorentzian holonomy algebras was obtained recently. In the present paper weakly-irreduci…

This paper classifies holonomy groups of K-contact sub-pseudo-Riemannian manifolds.

The classification of all possible holonomy algebras of Einstein and vacuum Einstein Lorentzian manifolds is obtained. It is shown that each such algebra appears as the holonomy algebra of an Einstein (resp., vacuum Einstein) Lorentzian manifold, the direct constructions are given. Also the holonomy algebras of totally…

The aim of this paper is to show that holonomy properties of Finsler manifolds can be very different from those of Riemannian manifolds. We prove that the holonomy group of a positive definite non-Riemannian Finsler manifold of non-zero constant curvature with dimension >2 cannot be a compact Lie group. Hence this holo…

The article proves a lower semicontinuity property of holonomy maps.

In order to understand the linearization problem around a leaf of a singular foliation, we extend the familiar holonomy map from the case of regular foliations to the case of singular foliations. To this aim we introduce the notion of holonomy transformation. Unlike the regular case, holonomy transformations can not be…

Study holonomy in pseudo-Hermitian geometry structures.

Our paper is devoted to the study of the holonomy groups of Finsler surfaces using the methods of infinite dimensional Lie theory. The notion of infinitesimal holonomy algebra will be introduced, by the smallest Lie algebra of vector fields on an indicatrix, containing the curvature vector fields and their horizontal c…