arXiv research

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

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

New examples show not all homology fiber bundles are topological.

Develops topological concepts for Morrey-Sobolev bundles in high dimensions.

This article reviews $\infty$-bundles and their applications in geometry and physics.

Kontsevich's classes distinguish smooth structures on fiber bundles.

New approach simplifies topological T-duality for torus bundles.

Classifies equivariant vector bundles over toric manifolds.

Extends Gelfand duality to various geometric and analytical categories.

We extend topological recursion to twisted Higgs bundles with singularities.

The transition maps for a Sobolev $G$-bundle are not continuous in the critical dimension and thus the usual notion of topology does not make sense. In this work, we show that if such a bundle $P$ is equipped with a Sobolev connection $A$, then one can associate a topological isomorphism class to the pair $\left( P, A\…

The paper proves metrizability and dynamics of Weil bundles.

Geodesic flow mixing on convex projective manifolds proven.

If a characteristic class for two vector bundles over the same base space does not coincide, then the bundles are not isomorphic. We give under rather common assumptions a lower bound on the topological dimension of the set of all points in the base over which a morphism between such bundles is not bijective. Moreover,…

Study the complexity of horizontality in 4-torus vector bundles.

We give a simplified definition of topological T-duality that applies to arbitrary torus bundles. The new definition does not involve Chern classes or spectral sequences, only gerbes and morphisms between them. All the familiar topological conditions for T-duals are shown to follow. We determine necessary and sufficien…

It is known that, for Dirac operators on Riemann surfaces twisted by line bundles with Hermitian-Einstein connections, it is possible to obtain estimates for the first eigenvalue in terms of the topology of the twisting bundle \cite{JL2}. Attempts to generalize topological estimates for higher rank bundles or higher di…

New spherical T-duality for higher degree forms in fiber bundles.

The work of Ray and Singer which introduced analytic torsion, a kind of determinant of the Laplacian operator in topological and holomorphic settings, is naturally generalized in both settings. The couplings are extended in a direct way in the topological setting to general flat bundles and in the holomorphic setting t…

We consider the problem of robot motion planning in an oriented Riemannian manifold as a topological motion planning problem in its oriented frame bundle. For this purpose, we study the topological complexity of oriented frame bundles, derive an upper bound for this invariant and certain lower bounds from cup length co…

Study Riemannian metric bundles and their connections to K-theory.

Matroid bundles, introduced by MacPherson, are combinatorial analogues of real vector bundles. This paper sets up the foundations of matroid bundles, and defines a natural transformation from isomorphism classes of real vector bundles to isomorphism classes of matroid bundles, as well as a transformation from matroid b…

Proves 3-manifold groups uniquely identify hyperbolic bundles.

In this paper we introduce the notion of almost flatness for (stably) relative bundles on a pair of topological spaces and investigate basic properties of it. First, we show that almost flatness of topological and smooth sense are equivalent. This provides a construction of an almost flat stably relative bundle by usin…

FibeRed reduces complex data dimensions while preserving topology.

We give a new proof of an index theorem for fiber bundles of compact topological manifolds due to Dwyer, Weiss, and Williams, which asserts that the parametrized $A$-theory characteristic of such a fiber bundle factors canonically through the assembly map of $A$-theory. Furthermore our main result shows a refinement of…

For a semisimple real Lie group $G$, we study topological properties of moduli spaces of polystable parabolic $G$-Higgs bundles over a Riemann surface with a divisor of finitely many distinct points. For a split real form of a complex simple Lie group, we compute the dimension of apparent parabolic Teichm{ü}ller compon…

The study classifies manifolds that can be split into two disk bundles.

In this paper we give a characterization of 2-dimensional topological field theories over a space $X$ as Frobenius bundles with connections over $LX$, the free loop space of $X$. This is a generalization of the folk theorem stating that 2-dimensional topological field theories (over a point) are described by finite-dim…

Researchers calculate the Ray-Singer Torsion for $S^{1}$ bundles.

We present a new infinite class of near-horizon geometries of degenerate horizons, satisfying Einstein's equations for all odd dimensions greater than five. The symmetry and topology of these solutions is compatible with those of black holes. The simplest examples give horizons of spatial topology S^3xS^2 or the non-tr…

We extend topological T-duality to the case of general circle bundles. In this setting we prove existence and uniqueness of T-duals. We then show that T-dual spaces have isomorphic twisted cohomology, twisted $K$-theory and Courant algebroids. A novel feature is that we must consider two kinds of twists in de Rham coho…

Equivariant T-duality connects bundles with twists.

Given a principal bundle over a closed manifold, G --> P --> M, let P^{Ad} --> M be the associated adjoint bundle. Gruher and Salvatore showed that the Thom spectrum (P^{Ad})^{-TM} is a ring spectrum whose corresponding product in homology is a Chas-Sullivan type string topology product. We refer to this spectrum as th…

We describe the second integral cohomology group of a surface bundle as the group of Chern classes of fiberwise holomorphic complex line bundles and use this to obtain information on this group.

This survey provides an introduction to basic questions and techniques surrounding the topology of the moduli space of stable Higgs bundles on a Riemann surface. Through examples, we demonstrate how the structure of the cohomology ring of the moduli space leads to interesting questions of a combinatorial nature.

The paper reformulates Legendrian contact homology using string topology.

The paper explores Higgs bundles and their moduli spaces on Riemann surfaces.

Geometric analysis on real analytic manifolds using seminorms.

Efficient algorithms for WRT invariants of torus bundles using algebraic structures.

Study on random surfaces in hyperbolic 3-manifolds, focusing on geometric and topological properties.

New spherical Milnor spaces for diffeological groups with geometric and topological properties.

New proof of Milnor-Wood inequality for circle bundles.

The paper studies weak singular Hermite-Einstein structures on homogeneous vector bundles.

Let $X$ be a compact connected Riemann surface of genus at least two, and let ${G}$ be a connected semisimple affine algebraic group defined over $\mathbb C$. For any $δ\in π_1({G})$, we prove that the moduli space of semistable principal ${G}$--bundles over $X$ of topological type $δ$ is simply connected. In contrast,…

We prove the existence of essential loops in the space of contact structures on torus bundles over the circle.

A new approach uses circuit topology to study complex polymer interactions.

New minimal hypersurfaces in 4D sphere found.