arXiv research

The paper studies conformal and projective structures using 2-frame bundles.

Holomorphic projective structures and bundles are studied on surfaces, revealing affine spaces of parameters.

We discuss conditions for the integrability of an almost complex structure defined on the total space of an induced Hopf S^3-bundle over a Sasakian manifold . As an application, we obtain an uncountable family of inequivalent complex structures on the Stiefel manifolds of orthonormal 2-frames in C^{n+1}, non compatible…

The Ooguri-Vafa space is a 4-dimensional incomplete hyperkähler manifold, defined on the total space of a singular torus fibration with one singular nodal fiber. It has been proposed that the Ooguri-Vafa hyperkähler metric should be part of the local model of the hyperkähler metric of the Hitchin moduli spaces, near th…

We prove Csorba's conjecture that the Lovász complex Hom(C_5,K_n) of graph multimorphisms from the 5-cycle C_5 to the complete graph K_n is Z/2Z-equivariantly homeomorphic to the Stiefel manifold, V(n-1,2), the space of (ordered) orthonormal 2-frames in R^{n-1}. The equivariant piecewise-linear topology that we need is…

This paper presents hyperbolic rank rigidity results for rank 1, nonpositively curved spaces. Let $M$ be a compact, rank 1 manifold with nonpositive sectional curvature and suppose that along every geodesic in $M$ there is a parallel vector field making curvature $-a^2$ with the geodesic direction. We prove that $M$ ha…

Develops finite-gap solutions for Pohlmeyer--Lund--Regge equation and Lund--Regge curve evolution.

We show that for any n > 3 there exists an equivalence functor from the category of n-fold connected simple coverings of B^3 x [0, 1] branched over ribbon surface tangles up to certain local ribbon moves, to the category Chb^{3+1} of orientable relative 4-dimensional 2-handlebody cobordisms up to 2-deformations. As a c…

We provide combinatorial realizations, according to the usual objects/moves scheme, of the following three topological categories: (1) pairs (M,v) where M is a 3-manifold (up to diffeomorphism) and v is a (non-singular vector) field, up to homotopy; here possibly the boundary of M is non-empty and v may be tangent to t…

Sedenions have geometric submanifolds with special properties.

We build a new probability measure on closed space and plane polygons. The key construction is a map, given by Knutson and Hausmann using the Hopf map on quaternions, from the complex Stiefel manifold of 2-frames in n-space to the space of closed n-gons in 3-space of total length 2. Our probability measure on polygon s…

The study of quotient structures in multi-graded bundles, including double vector bundles.

Study of semi-principal bundles using group actions and wreath products.

Establishes a framework for stringor bundles, proving their canonical isomorphism to Stolz-Teichner's.

In this study, we generalize double tangent bundles to double jet bundles. We present a secondary vector bundle structure on a 1-jet of a vector bundle. We show that 1-jet of a vector bundle carries two vector bundle structures, namely primary and secondary structures. We also show that the manifold charts induced by p…

This paper shows vector bundles and differential bundles are equivalent in smooth manifolds.

Introduces Darboux-Lie derivative for fiber bundles.

On a complex manifold, a co-Higgs bundle is a holomorphic vector bundle with an endomorphism twisted by the tangent bundle. The notion of generalized holomorphic bundle in Hitchin's generalized geometry coincides with that of co-Higgs bundle when the generalized complex manifold is ordinary complex. Schwarzenberger's r…

A stratified bundle is a fibered space in which strata are classical bundles and in which attachment of strata is controlled by a structure category of fibers. Well known results on fibre bundles are shown to be true for stratified bundles; namely the pull back theorem, the bundle theorem and the principal bundle theor…

We define double principal bundles (DPBs), for which the frame bundle of a double vector bundle, double Lie groups and double homogeneous spaces are basic examples. It is shown that a double vector bundle can be realized as the associated bundle of its frame bundle. Also dual structures, gauge transformations and conne…

Proves every equivariant vector bundle over toric manifolds is a Klyachko bundle.

Categorical bundles provide a natural framework for gauge theories involving multiple gauge groups. Unlike the case of traditional bundles there are distinct notions of triviality, and hence also of local triviality, for categorical bundles. We study categorical principal bundles that are product bundles in the categor…

Symplectic fillings of prequantization bundles are shown to be disk bundles under certain conditions.

Identifies images of determinant morphism for specific co-Higgs bundles.

Bundling of graph edges (node-to-node connections) is a common technique to enhance visibility of overall trends in the edge structure of a large graph layout, and a large variety of bundling algorithms have been proposed. However, with strong bundling, it becomes hard to identify origins and destinations of individual…

Study projective flat vector bundles over Riemann surfaces using Wronskian line bundles.

The paper defines and explores vector bundles that can be turned and their properties.

The paper generalizes bundle gerbes over groupoids and their correspondence with PB groupoids.

Study geometric characterization of asymptotic pseudodifferential calculus on spinor bundles.

Generalizes Higgs bundles theory using a vector bundle twist.

Study of generalized vector bundles and their geometric tools.

The paper extends orthogonal decomposition results to hermitian Higgs bundles.

We present the notion of a filtered bundle as a generalisation of a graded bundle. In particular, we weaken the necessity of the transformation laws for local coordinates to exactly respect the weight of the coordinates by allowing more general polynomial transformation laws. The key examples of such bundles include af…

Introduces generalized principal bundles and connections, linking them to standard gauge theories.

Study proves existence of precotangent bundles for Grassmannians.

Investigates connections in Lie group bundles, focusing on geometric reduction.

Study of Pascal algebra matrices and their jet bundle map for vector bundles.

A bundle gerbe is constructed from an oriented smooth vector bundle of even rank with a fiberwise inner product, over a compact connected orientable smooth manifold with Riemannian metric. From a trivialization of the bundle gerbe is constructed an irreducible Clifford module bundle, a spinor bundle over the smooth fre…

We develop the theory of smooth principal bundles for a smooth group $G$, using the framework of diffeological spaces. After giving new examples showing why arbitrary principal bundles cannot be classified, we define $D$-numerable bundles, the smooth analogs of numerable bundles from topology, and prove that pulling ba…

In \cite{BR1}, \cite{BR2}, a parabolic determinant line bundle on a moduli space of stable parabolic bundles was constructed, along with a Hermitian structure on it. The construction of the Hermitian structure was indirect: The parabolic determinant line bundle was identified with the pullback of the determinant line b…

Study on topological rigidity of ALE vector bundles with specific conditions.

Defines connections for singularly foliated bundles.

Extends Higgs fields theory to complex fiber bundles.

Study improves Simpson's estimate for cyclic harmonic bundles.

This masters thesis reviews bundle gerbe theory and the well-known basic bundle gerbe over SU(n). We introduce the cup product bundle gerbe, and show it is stably isomorphic to the pullback of the basic bundle gerbe by the Weyl map. This result enriches our understanding of the basic bundle gerbe, which has numerous ap…

Graded bundles are a class of graded manifolds which represent a natural generalisation of vector bundles and include the higher order tangent bundles as canonical examples. We present and study the concept of the linearisation of graded bundle which allows us to define the notion of the linear dual of a graded bundle.…

Decomposes bundle gerbes on supermanifolds into simpler components.

Study shows some biquotients have non-biquotient tangent bundles.