Characterizes group connections on group bundles.
problem Understanding connections on group bundles.
method Characterizes connections as affine spaces and uses the Ambrose-Singer theorem.
result Group connections form an affine space over cocycles.
On-device research index
arXiv research
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.
168,695 papers · 148 categories
Trend · papers per month
48 results for “group bundles”
Study of semi-principal bundles using group actions and wreath products.
problem Understanding bundles with fibers as free -spaces.
method Defining semi-principal bundles, bases, and frame bundles; using wreath products and functors.
result Semi-principal bundles can be retracted to principal bundles, preserving parallel transport.
Investigates connections in Lie group bundles, focusing on geometric reduction.
problem Geometric reduction of gauge field theories.
method Definition and analysis of equivariant connections in Lie group bundles.
result Provides conditions for the existence and properties of equivariant connections.
We consider various generalisations of the string class of a loop group bundle. The string class is the obstruction to lifting a bundle whose structure group is the loop group to one whose structure group is the Kac-Moody central extension of the loop group. We develop a notion of higher string classes for bundles…
New smooth 2-group extensions from bundle gerbes on manifolds.
problem Classifying equivariant structures on bundle gerbes.
method Global approach to parallel transport, homotopy-coherent associated bundle construction.
result New models for the string group of compact simply-connected Lie groups.
Study simplicial volume in fiber bundles with connected groups.
problem Understanding simplicial volume in fiber bundles.
method Investigated fiber bundles with connected structure groups.
result Simplicial volume of total space matches trivial bundle under certain conditions.
We consider trivializations of second iterated bundles of a Lie group that preserve lifted group structures. With such a trivialization, we elaborate Hamiltonian dynamics on cotangent, Lagrangian dynamics on tangent bundles and, both Hamiltonian and Lagrangian dynamics on Tulczyjew's symplectic space which is tangent o…
Introduces generalized principal bundles and connections, linking them to standard gauge theories.
problem Generalized principal bundles and connections in field theories.
method Local coordinate transformation laws and horizontal lifts.
result Generalized principal connections are associated to Lie group fiber bundle connections.
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.
Study finite group actions on Higgs bundle moduli spaces.
problem Describe fixed points of finite group actions on Higgs bundle moduli spaces.
method Use twisted Γ-equivariant bundles and Prym-Narasimhan-Ramanan construction.
result Provide description of fixed-point subvarieties of certain finite group actions on G-character varieties.
Explicit String bundlesmath.DG
Method constructs 2-bundles over homogeneous spaces.
problem Lack of explicit examples of 2-bundles with specific structure groups.
method Constructs 2-bundles over homogeneous spaces using a method outlined.
result Explicit formulas for Cech cocycles are provided.
Multiplicative bundle gerbes are gerbes over a Lie group which are compatible with the group structure. In this article connections on such bundle gerbes are introduced and studied. It is shown that multiplicative bundle gerbes with connection furnish geometrical constructions of the following objects: smooth central e…
We prove that all smooth sphere bundles that admit fiberwise 1/4-pinched metrics are induced bundles of vector bundles, so their structure groups reduce from the diffeomorphism group of the sphere to the orthogonal group. This result implies the existence of many smooth n-sphere bundles over a k-sphere that do not supp…
Pseudo-Anosov subgroups in surface bundles over tori are convex cocompact.
problem Understanding the structure of pseudo-Anosov subgroups in surface bundles over tori.
method Using the Birman exact sequence to show convex cocompactness.
result Finitely generated, purely pseudo-Anosov subgroups are convex cocompact in surface bundles over tori.
Constructs 2-representations and 2-vector bundles for Lie 2-groups.
problem No strict model for string 2-group, so coherent model is constructed.
method Builds category of 2-representations and equivariant 2-vector bundles.
result Explicit formulas for 2-representations and 2-vector bundles.
The stringor bundlemath.AT
Establishes a framework for stringor bundles, proving their canonical isomorphism to Stolz-Teichner's.
problem Defining and rigorously studying higher differential geometric objects like stringor bundles.
method Developed a framework of 2-Hilbert bundles, including an associated bundle construction.
result Proves the Stolz-Teichner stringor bundle is canonically isomorphic to the 2-Hilbert bundle.
In this paper we describe how one can obtain Lie group structures on the group of (vertical) bundle automorphisms for a locally convex principal bundle P over the compact manifold M. This is done by first considering Lie group structures on the group of vertical bundle automorphisms Gau(P). Then the full automorphism g…
Discrete connections on abelian Lie groups bundles are studied.
problem Understanding discrete connections on abelian Lie group principal bundles.
method Formalized discrete connections as singular cochains and proved a discrete holonomy formula.
result Discrete connections on abelian Lie group bundles have properties similar to continuous connections.
Study group extensions and bundles on manifolds.
problem Understanding group extensions and their relation to bundles on manifolds.
method Establish and study a correspondence between extensions and equivariant bundles using non-abelian cohomology.
result A correspondence between -bundles and twisted -equivariant bundles on Galois -coverings.
Introduces Lie semiheaps and their relation to Lie groups and bundles.
problem Defining and understanding Lie semiheaps and their properties.
method Introducing Lie semiheaps and proving their properties in relation to Lie groups and bundles.
result Established the existence of left-invariant vector fields on Lie semiheaps.
Gerbes and Lie Groupsmath.DG
We present a review of bundle gerbes, emphasizing their relations to Lie groups. Indeed, compact Lie groups do not only carry the structure of a Riemannian manifold, but also canonical families of bundle gerbes. We recall the construction of these bundle gerbes and their relation to loop groups. We discuss several alge…
Classifies very stable Higgs bundles for complex groups.
problem Classifying Higgs bundles for arbitrary complex groups.
method Classification based on stability and Higgs field properties.
result Extends previous classification for GLn to arbitrary groups.
Study Lie algebroid connections on principal bundles over complex projective varieties.
problem Existence and properties of Lie algebroid connections on principal bundles.
method Definition and study of Lie algebroid valued connections on holomorphic principal G-bundles, investigation of existence criteria.
result Investigation of criteria for existence of Lie algebroid connections on principal G-bundles over smooth complex projective curves.
The paper classifies metrics on a Heisenberg group's cotangent bundle.
problem Classifying Riemannian metrics on a Heisenberg group's cotangent bundle.
method Left-invariant Riemannian metrics classification and uniqueness proof.
result Complex structure is unique and pseudoKähler metrics are Ricci flat.
Atoroidal surface bundlesmath.GT
New examples of surface bundles found over surfaces.
problem Finding compact atoroidal surface bundles.
method Type-preserving homomorphism from knot complement to mapping class group.
result Infinitely many commensurability classes of surface subgroups.
Turaev-Viro invariants match for certain surface bundles.
problem Matching Turaev-Viro invariants for surface bundles.
method Profinite completions and spherical fusion categories.
result Invariants coincide for specific surface groups.
We discuss nonabelian bundle gerbes and their differential geometry using simplicial methods. Associated to any crossed module there is a simplicial group NC, the nerve of the 1-category defined by the crossed module and its geometric realization |NC|. Equivalence classes of principal bundles with structure group |NC| …
Survey on Higgs bundle moduli spaces and their connected components.
problem Counting connected components of Higgs bundle moduli spaces.
method Analyzes moduli spaces for Higgs bundles associated with real Lie groups and closed Riemann surfaces.
result Explicit descriptions of some moduli space components are possible.
Proves 3-manifold groups uniquely identify hyperbolic bundles.
problem Identifying hyperbolic 3-manifold groups from their finite quotients.
method Upgraded Liu's result to detect fiber type via profinite completion.
result Proves hyperbolic bundles are distinguished by their profinite completions.
Let be a Lie group and $G\to\Aut(G)$ be the canonical group homomorphism induced by the adjoint action of a group on itself. We give an explicit description of a 1-1 correspondence between Morita equivalence classes of, on the one hand, principal 2-group $[G\to\Aut(G)]$-bundles over Lie groupoids and, on the other …
New complex structures found on tangent bundles of Lie groups.
problem Finding integrable complex structures on tangent bundles of Lie groups.
method Inspired by Samelson's construction, a left-invariant integrable almost complex structure is defined on the tangent bundle of any compact Lie group.
result Tangent bundles of compact Lie groups admit left-invariant integrable almost complex structures.
The paper examines the boundedness of bundle diffeomorphism groups over a circle.
problem Investigating the boundedness of bundle diffeomorphism groups over a circle.
method Distinguishing an integer k and constructing a function to analyze the bundle diffeomorphism group.
result The bundle diffeomorphism group is uniformly perfect when k ≥ 1 and unbounded when k = 0.
On the fundamental groups of effective compact Kähler orbifolds with nef anticanonical bundlemath.AG
Fundamental groups of certain Kähler orbifolds have polynomial growth.
problem Understanding the fundamental groups of specific types of orbifolds.
method Analyzing the orbifold fundamental group with respect to the nef anticanonical bundle.
result The orbifold fundamental group has polynomial growth.
This paper simplifies jet bundles of Lie group-valued functions using linear connections.
problem Trivializing jet bundles of Lie group-valued functions for easier computation.
method Utilizing a linear connection to trivialize into a vector bundle over .
result Explicit expressions for groupoid multiplication and inverse elements are provided.
Proves existence of flat connection on theta functions for G-bundles.
problem Existence of flat connections on nonabelian theta functions for G-bundles.
method Proves existence of a flat projective connection on nonabelian theta functions on moduli space of parabolic G-bundles.
result Existence of a flat projective connection on nonabelian theta functions for parabolic G-bundles.
Axis bundles in free-by-cyclic groups have non-generic monodromies.
problem Characterizing monodromies in free-by-cyclic groups.
method Analyzing monodromy actions on outer space and using properties of axis bundles.
result Monodromies having a 'lone axis' are non-generic and projectively discrete.
New method constructs degenerate Sasakian manifolds from hyperkähler bundles.
problem Constructing degenerate --Sasakian manifolds.
method Using fiber products of Boothby-Wang bundles over hyperkähler manifolds.
result No non-trivial compact examples exist, and one family of nilpotent Lie groups with this geometry is identified.
We prove the vanishing of a certain characteristic class of flat vector bundles when the structure groups of the bundles are contained in GL(N,Z). We do so by explicitly writing the characteristic class as an exact form on the base of the bundle.
In gauge theory, the Faddeev-Mickelsson-Shatashvili anomaly arises as a prolongation problem for the action of the gauge group on a bundle of projective Fock spaces. In this paper, we study this anomaly from the point of view of bundle gerbes and give several equivalent descriptions of the obstruction. These include li…
In this paper we investigate bundles whose structure group is the loop group LU(n). Our main result is to give a necessary and sufficient criterion for there to exist a Fourier type decomposition of such a bundle . This is essentially a decomposition of as , where is a finite dimensional…
Lie groups of automorphisms of cotangent bundles of Lie groups are completely characterized and interesting results are obtained. We give prominence to the fact that the Lie groups of automorphisms of cotangent bundles of Lie groups are super symmetric Lie groups. In the cases of orthogonal Lie lgebras, semi-simple Lie…
Study shows how certain curved bundles reduce their structure group.
problem Understanding how curvature affects bundle structure.
method Analyzes bundles with fibers as real projective spaces and positive curvature metrics.
result Structure group of bundles reduces when fibers have specific curvature properties.
Paper finds generalized torsions in non-bi-orderable 3-manifold groups.
problem Finding non-bi-orderable 3-manifold groups.
method Analyzing fundamental groups of once punctured torus bundles.
result Identifies generalized torsions in non-bi-orderable groups.
The paper calculates the mapping class group of specific complex projective plane bundles.
problem Computing the mapping class group of complex projective plane bundles.
method Analyzes sphere bundles of real vector bundles over .
result Calculates the mapping class group for specific examples like Milnor hypersurfaces.
In this work, we describe how to obtain the structure of an infinite-dimensional Lie group on the group of compactly carried bundle automorphisms Autc(P) for a locally convex prinicpal bundle P over a finite-dimensional smooth sigma-compact base M. This is a generalization of previous work by Wockel, where the base M w…
The paper constructs a free abelian group from Anosov representations on bundles.
problem Constructing a free abelian group from Anosov representations on bundles.
method Extending the -action via to the space of connections on pullbacks of tangent bundles.
result A free abelian group is constructed and acts properly discontinuously on it.
Lie-Yamaguti Algebra Bundlemath.RA
Introduces Lie-Yamaguti algebra bundles and their cohomology.
problem Defining and studying Lie-Yamaguti algebra bundles.
method Defined Lie-Yamaguti algebra bundles and their cohomology groups.
result Lie-Yamaguti algebra bundles naturally arise from geometric considerations.
The space of smooth sections of a symplectic fiber bundle carries a natural symplectic structure. We provide a general framework to determine the momentum map for the action of the group of bundle automorphism on this space. Since, in general, this action does not admit a classical momentum map, we introduce the more g…