arXiv research

Study hermitian Yang-Mills connections on pullback bundles for holomorphic submersions.

Commutes Pansu pullback with spectral complexes in Carnot groups.

Study the pullbacks and blowups of Lie algebroids and related structures.

Spectral sequence analysis for Sobolev mappings in Carnot groups.

Criterion for lifting smooth contact maps between Carnot groups to central extensions.

Sobolev mappings preserve the Rumin complex on contact manifolds.

This paper improves probabilistic latent models on hyperbolic spaces.

PFM generates novel samples on data manifolds using pullback geometry.

This paper introduces tangent display maps to simplify tangent category theory.

Adopting the pullback approach to global Finsler geometry, the aim of the present paper is to provide new intrinsic (coordinate-free) proofs of intrinsic versions of the existence and uniqueness theorems for the Cartan and Berwald connections on a Finsler manifold. To accomplish this, the notions of semispray and nonli…

The paper introduces new functors for cohomology groups of manifolds.

We show how the tangent functor extends from ordinary smooth maps to "microformal morphisms" (also called "thick morphisms") of supermanifolds. Microformal morphisms generalize ordinary maps and correspond to formal canonical relations between the cotangent bundles specified by generating functions depending on positio…

Extends symphonic maps to bi-symphonic maps between Riemannian manifolds.

We introduce mappings between spaces of functions on (super)manifolds that generalize pullbacks with respect to smooth maps but are, in general, nonlinear (actually, formal). The construction is based on canonical relations and generating functions. (The underlying structure is a formal category, which is a "thickening…

Study of permutational wreath pullbacks and their properties.

Study on mappings between nonrigid Carnot groups, proving quasisymmetric rigidity.

Proposes a scalable framework for extracting data manifold geometry.

Symplectic forms match on circle pattern space.

We present a family of complexes playing the same role, for homogeneous variational problems, that the horizontal parts of the variational bicomplex play for variational problems on a fibred manifold. We show that, modulo certain pullbacks, each of these complexes (apart from the first one) is globally exact. All the c…

We study a generalized functional related to the pullback metrics (3). We derive the first variation formula which yield stationary maps. We introduce the stress-energy tensor which is naturally linked to conservation law and yield monotonicity formula via the coarea formula and comparison theorem in Riemannian geometr…

Associated to a Thurston map $f: S^2 \to S^2$ with postcritical set $P$ are several different invariants obtained via pullback: a relation on the set of free homotopy classes of curves in $S^2- P$, a linear operator on the free $\R$-module generated by these homotopy classes of curves, a virtual endomorphism on the pur…

New construction of Atiyah and Todd classes for Lie pair pullback dg Lie algebroids.

New distances for comparing multivariate normal distributions.

We prove a generalization of Kawai theorem for the case of orbifold Riemann surface. The computation is based on a formula for the differential of a holomorphic map from the cotangent bundle of the Teichmüller space to the $\mathrm{PSL}(2,\mathbb{C})$-character variety, which allows to evaluate explicitly the pullback …

Lean 4 formalizes Stokes' theorem for smooth singular cubes.

Study on hermitian Yang-Mills connections on blown-up manifolds.

To a closed Riemannian manifold, we associate a set of (special values of) a family of Dirichlet series, indexed by functions on the manifold. We study the meaning of equality of two such families of spectral Dirichlet series under pullback along a map. This allows us to give a spectral characterization of when a smoot…

We extend the category of (super)manifolds and their smooth mappings by introducing a notion of microformal or "thick" morphisms. They are formal canonical relations of a special form, constructed with the help of formal power expansions in cotangent directions. The result is a formal category so that its composition l…

Adjusting conventional Chern-Simons theory to ${\rm G}_2$-manifolds, one describes ${\rm G}_2$-instantons on bundles over a certain class of $7$-dimensional flat tori which fiber non-trivially over $T^4$, by a pullback argument. Moreover, if $c_2\neq0$, any (generic) deformation of the ${\rm G}_2$-structure away from s…

Develops analysis of Hölder continuous mappings on Heisenberg groups.

A new connection in Finsler geometry unifies various types of connections.

This work develops methods to analyze data on curved spaces using deep learning.

Article studies symmetry in smooth vector bundles using advanced operations.

We obtain universal models for several types of locally conformal symplectic manifolds via pullback or reduction. The relation with recent embedding results for locally conformal Kähler manifolds is discussed.

Study compactness and continuity in Sobolev wave front set spaces for smooth vector bundles.

We study a regular closure operator in the category of quandles. We show that the regular closure operator and the pullback closure operator corresponding to the reflector from the category of quandles to its full subcategory of trivial quandles coincide, we give a simple description of this closure operator, and analy…

We give a geometric obstruction to the non-negativity of the sectional curvature in the total spaces of certain Riemannian submersions with totally geodesic fibers; applications of this obstruction to several examples are given.

DiffeoCFM efficiently generates realistic brain connectivity matrices using pullback metrics.

Using a Heegaard diagram for the pullback of a knot $K \subset S^3$ in its cyclic double branched cover $Σ_2(K)$, we give a combinatorial proof for the invariance of knot Floer homology over $\mathbb{Z}$.

The paper proves stability of pulled back parabolic bundles on curves.

The canonical metric on a Riemann surface is the pullback from the Euclidean metric on the Jacobian variety via the period map. We study its induced L^2 metric on Teichmuller space via a variational approach.

Finite vector bundles over complex manifolds are trivializable via finite covers.

The Novikov complex of a circle-valued Morse function is constructed algebraically from the Morse-Smale complex of the restriction to a fundamental domain of the real-valued Morse function on the pullback infinite cyclic cover.

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…

The aim of the present paper is to provide an \emph{intrinsic} investigation of the properties of the most important geometric objects associated with the fundamental linear connections in Finsler geometry. We investigate intrinsically the most general relations concerning the torsion tensor fields and the curvature te…

The pullback approach to global Finsler geometry is adopted. Some new types of special Finsler spaces are introduced and investigated, namely, Ricci, generalized Ricci, projectively recurrent and m-projectively recurrent Finsler spaces. The properties of these special Finsler spaces are studied and the relations betwee…

Introduces new Finsler metrics and connects them to information geometry.

The construction of a linear connection on a pullback bundle from a connection on a vector bundle is explained in terms of fiberwise linear approximation. This procedure clarifies the geometric meaning of the linearized connection as well as the associated parallel transport and curvature.