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.
Smooth approximations of Lipschitz maps via Ehresmann fibrations and Reeb sphere theorem for functions.
Extends connections on Lie groupoids, proving completeness conditions.
Study finds conditions for finite-dimensional Lie group structure in basic automorphism groups of certain Cartan foliations.
A degree 1 non-negative graded super manifold equipped with a degree 1 vector field Q satisfying [Q, Q]=1, namely a so-called NQ-1 manifold is, in plain differential geometry language, a Lie algebroid. We introduce a notion of fibration for such super manifols, that essentially involves a complete Ehresmann connection.…
We study Riemannian metrics on Lie groupoids in the relative setting. We show that any split fibration between proper groupoids can be made Riemannian, and we use these metrics to linearize proper groupoid fibrations. As an application, we derive rigidity theorems for Lie groupoids, which unify, simplify and improve si…
The paper develops a theory of Ehresmann structures in positive characteristic.
Constructs Higgs bundle moduli spaces using Teichmüller space.
Ehresmann connections in tangent categories
Constructs covariant derivatives for Ehresmann connections.
Study of Hitchin moduli spaces over Teichmüller space.
Develops theory of multiplicative Ehresmann connections for Lie groupoids.
In the present work we provide a constructive method to describe contact structures on compact homogeneous contact manifolds. The main feature of our approach is to describe the Cartan-Ehresmann connection (gauge field) for principal circle bundles over complex flag manifolds by using elements of representation theory …
Study of symplectic trivialization and reduction of bundles with symmetry and connection.
Jets of mappings introduced by Ehresmann are still the most useful objects for formulating geometric frameworks of physical theories. We are proposing modifications designed to make jet theory less dependent on local coordinates. Extensions of the theory with applications to the calculus of variations and mechanics are…
In this paper, we define conservative semibasic vector forms on the tangent bundle of a Finsler manifold. Using these vector forms, we characterize conservative Ehresmann connections with respect to the energy function. Then we find a correspondence between torsion-free semibasic vector forms and the su…
In this paper the author determines necessary and sufficient conditions for existence of the Ehresmann connection on a manifold foliated by locally free action of the commutative Lie group. Also here we describe structure of for a leaf in case such a connection exists. Finally we give some res…
Extends Yang-Mills theory to non-integrable Lie algebroids.
Study geometric structures on LVM threefolds, focusing on resonant structures.
The word `double' was used by Ehresmann to mean `an object X in the category of all X'. Double categories, double groupoids and double vector bundles are instances, but the notion of Lie algebroid cannot readily be doubled in the Ehresmann sense, since a Lie algebroid bracket cannot be defined diagrammatically. In this…
We describe recent links between two topics: geometric structures on manifolds in the sense of Ehresmann and Thurston, and dynamics "at infinity" for representations of discrete groups into Lie groups.
Develops a reduction theory for covariant field theories with gauge symmetries.
This paper studies covariant derivatives for Lie groupoids with representation-valued forms.
This paper illustrates the themes of the title in terms of: van Kampen type theorems for the fundamental groupoid; holonomy and monodromy groupoids; and higher homotopy groupoids. Interaction with work of the writer is explored.
For a smooth (locally trivial) principal bundle in Ehresmann's sense, the relation between the commuting vertical and horizontal actions of the structural Lie group and the structural Lie groupoid (isomorphisms between vertical fibers) is regarded as a special case of a symmetrical concept of conjugation between "princ…
We put together some of the efforts by several people of making aspects of fibre bundle theory into algebra. The initiator of these efforts was Charles Ehresmann, who put the notion of groupoid and groupoid action in the focus of fibre bundle theory in general, and in connection theory in particular.
In sub-Riemannian geometry the coefficients of the Jacobi equation define curvature-like invariants. We show that these coefficients can be interpreted as the curvature of a canonical Ehresmann connection associated to the metric, first introduced in [Zelenko-Li]. We show why this connection is naturally nonlinear, and…
Novel generalization of principal bundles using Lie groupoids.
Every smooth fiber bundle admits a complete (Ehresmann) connection. This result appears in several references, with a proof on which we have found a gap, that does not seem possible to remedy. In this note we provide a definite proof for this fact, explain the problem with the previous one, and illustrate with examples…
A canonical connection is attached to any k-symplectic manifold. We study the properties of this connection and its geometric applications to k-symplectic manifolds. In particular we prove that, under some natural assumption, any ksymplectic manifold admits an Ehresmann connection, discussing some corollaries of this r…
Develops a Kaluza-Klein theory in affine spaces without metric.
We present a multisymplectic formulation of the Yang--Mills equations. The connections are represented by normalized equivariant 1-forms on the total space of a principal bundle, with values in a Lie algebra. Within the multisymplectic framework we realize that, under reasonable hypotheses, it is not necessary to assum…
We provide a framework for extensions of Lie algebroids, including non-abelian extensions and Lie algebroids over different bases. Our approach involves Ehresmann connections, which allows straight generalizations of classical constructions. We exhibit a filtration in cohomology and explain the associated spectral sequ…
Study nondegenerate fibrations of Euclidean spaces and their relation to sphere fibrations.
Introduces new stability concept for Fano fibrations.
Singular fibrations over surfaces generalize Lefschetz fibrations and have new construction methods.
Study of line fibrations in R^3, focusing on non-skew cases.
Lie algebroids are by no means natural as an infinitesimal counterpart of groupoids. In this paper we propose a functorial construction called Nishimura algebroids for an infinitesimal counterpart of groupoids. Nishimura algebroids, intended for differential geometry, are of the same vein as Lawvere's functorial notion…
We compare two ways of interpreting higher order connections. The geometric approach lies in the decomposition of higher order tangent space into the horizontal and vertical structures while the jet--like approach considers a higher order connection as the section of a jet prolongation of a fibered manifold. Particular…
Third in a series, this paper constructs non-trivial Cayley fibrations with conical singularities.
Paper proves achiral Lefschetz fibrations from non-orientable Lefschetz fibrations.
The paper constructs Sasakian lifts from Kähler manifolds and studies their properties.
Contact structures are induced by nondegenerate skew fibrations of R^3.
Auroux, Donaldson and Katzarkov introduced broken Lefschetz fibrations as a generalization of Lefshcetz fibrations in order to describe near-symplectic 4-manifolds. We first study monodromy representations of higher sides of genus-1 simplified broken Lefschetz fibrations. We then completely classify diffeomorphism type…
Same genus-2 fibration structures for specific types found by different researchers.
Constructs new coassociative fibrations for G2 manifolds.
We show that generalized broken fibrations in arbitrary dimensions admit rank-2 Poisson structures compatible with the fibration structure. After extending the notion of wrinkled fibration to dimension 6 we prove that these wrinkled fibrations also admit compatible rank-2 Poisson structures. In the cases with indefinit…
Study fibrations over with same singularities, showing monodromies are equivalent up to direct sums.
The paper proves finiteness for stable Lagrangian fibrations with a given divisor.