arXiv research

Category theory generalizes finite type invariants using diagrams systems.

Generalized Roter type manifold is a generalization of conformally flat manifold as well as Roter type manifold, which gives rise the form of the curvature tensor in terms of algebraic combinations of the fundamental metric tensor and Ricci tensors upto level 2. The object of the present paper is to investigate the cha…

We analyze Darboux transformations in very general settings for multidimensional linear partial differential operators. We consider all known types of Darboux transformations, and present a new type. We obtain a full classification of all operators that admit Wronskian type Darboux transformations of first order and a …

The generic fiber of a Lagrangian fibration on an irreducible holomorphic symplectic manifold is an abelian variety. Associate a polarization type to such Lagrangian fibrations coming from polarizations on a generic fiber. We prove that this polarization type is constant in families of Lagrangian fibrations. Further, w…

The paper describes a specific type of Kähler surfaces.

Study on types of generalized hypercomplex structures on tori and Kodaira-Thurston surface.

We describe a bordered version of totally twisted Khovanov homology. We first twist Roberts's type $D$ structure by adding a "vertical" type $D$ structure which generalizes the vertical map in twisted tangle homology. One of the distinct advantages of our type $D$ structure is that it is homotopy equivalent to a type $…

4-manifolds with specific groups have unique homotopy types.

New Lie groups generalize H-type groups with nondegenerate centers.

Despite the great success of deep neural networks, the adversarial attack can cheat some well-trained classifiers by small permutations. In this paper, we propose another type of adversarial attack that can cheat classifiers by significant changes. For example, we can significantly change a face but well-trained neural…

Generates special homeomorphisms for complex surfaces.

In~\cite{Kim} the author generalized the Conway algebra and constructed the invariant valued in the generalized Conway algebra defined by applying two skein relations to crossings, which is called a generalized Conway type invariant. The generalized Conway type invariant is a generalization of Homflypt polynomial. In t…

Researchers generalize Ribaucour-type surfaces with new mathematical representation.

The paper derives inequalities on Finsler manifolds, influenced by their curvatures.

The paper studies curvature tensors and hypersurfaces in Kenmotsu type manifolds.

In this paper we give classification of Kähler surfaces of generalized Calabi type.

Proves two theorems on odd-dimensional manifolds with boundary.

In this paper, we prove an equivariant Kastler-Kalau-Walze type theorem for spin manifolds without boundary. For $6$ dimensional spin manifolds with boundary, we also give an equivariant Kastler-Kalau-Walze type theorem. Then we generalize this theorem to the general $n$ dimensional manifold. An equivariant Kastler-Kal…

Paper proves a Liouville theorem for a generalized elliptic equation on H-type groups.

We prove that a compact smooth 4-manifold admits generalized complex structures of odd type if and only if it has a transversely holomorphic 2-foliation. Consequently, there exist generalized complex structures of odd type on a circle bundle over a closed Seifert fibered 3-manifold.

Generative model synthesizes complex data structures with composite and nested types.

The category of generalized Lie algebroids is presented. We obtain an exterior differential calculus for generalized Lie algebroids. In particular, we obtain similar results with the classical and modern results for Lie algebroids. So, a new result of Maurer-Cartan type is presented. Supposing that any vector subbundle…

Paper solves the minimal generating set problem for singular Reidemeister moves.

Minimal generating sets of Reidemeister moves identified and classified.

Study harmonicity of metrics in generalized Kantowski-Sachs spacetime.

We study type one generalized complex and generalized Calabi--Yau manifolds. We introduce a cohomology class that obstructs the existence of a globally defined, closed 2-form which agrees with the symplectic form on the leaves of the generalized complex structure, the twisting class. We prove that in a compact, type on…

The paper proves properties of Kähler surfaces with zero scalar curvature.

This thesis introduces big mapping class groups and their structure.

Study of CB generating sets for infinite-type surfaces.

It is known that all left-invariant pseudo-Riemannian metrics on $H_3$ are algebraic Ricci solitons. We consider generalizations of Riemannian $H$-type, namely pseudo$H$-type and $pH$-type. We study algebraic Ricci solitons of left-invariant Lorentzian metrics on 2-step nilpotent Lie groups of both types.

We propose a definition of the Toledo invariant for representations of fundamental groups of smooth varieties of general type into semisimple Lie groups of Hermitian type. This definition allows to generalize the results known in the classical case of representations of complex hyperbolic lattices to this new setting: …

Extends A-type coefficient polynomials to B-type setting, introducing new invariants.

The paper provides gradient estimates for nonlinear heat-type equations on smooth metric measure spaces.

We prove that for any $n\geq 4$ there are infinitely many real homotopy types of $2n$-dimensional nilmanifolds admitting generalized complex structures of every type $k$, for $0 \leq k \leq n$. This is in deep contrast to the $6$-dimensional case.

We establish a general Liouville type theorem for conformally invariant fully nonlinear equations.

We introduce a special class of nilpotent Lie groups of step 2, that generalizes the so called $H$(eisenberg)-type groups, defined by A. Kaplan in 1980. We change the presence of inner product to an arbitrary scalar product and relate the construction to the composition of quadratic forms. We present the geodesic equat…

An exterior differential calculus in the general framework of generalized Lie algebroids is presented. A theorem of Maurer-Cartan type is obtained. All results with details proofs are presented and a new point of view over exterior differential calculus for Lie algebroids is obtained. Using the theory of linear connect…

Local equivalence found between certain solitons and generalized Kähler-Ricci solitons.

Big mapping class groups of infinite type surfaces have infinite asymptotic dimension.

GDA-HIN adapts across heterogeneous networks by aligning shared and private node types.

In this paper we consider all possible generalizations of the B-type Hecke algebras, namely the cyclotomic and what we call 'generalized', and we construct Markov traces on each of them, so as to obtain all possible different levels of homfly-pt analogues in the solid torus related to the (Hecke) algebras of B-type.

We prove that H-type Carnot groups of rank $k$ and dimension $n$ satisfy the $\mathrm{MCP}(K,N)$ if and only if $K\leq 0$ and $N \geq k+3(n-k)$. The latter integer coincides with the geodesic dimension of the Carnot group. The same result holds true for the larger class of generalized H-type Carnot groups introduced in…

In this paper, we establish some general Kastler-Kalau-Walze type theorems for any dimensional manifolds with boundary which generalize the results in [WW1].

Landweber and Stong prove that if a closed spin manifold $M$ admits a smooth $S^1$-action of odd type, then its signature $\mathrm{sign}(M)$ vanishes. In this paper, we extend the result to a torus action on a closed oriented manifold with generalized odd type.

We prove a Frobenius-type theorem for singular distributions generated by a family of locally Lipschitz continuous vector fields satisfying almost everywhere a quantitative finite type condition.

Preprint proves quantum coideal Schur-Weyl duality and generalizes Jones-Wenzl projectors.

In this paper, we establish two Santaló type formulas for general Finsler manifolds. As applications, we derive a universal lower bound for the first eigenvalue of the nonlinear Laplacian, two Croke type isoperimetric inequalities, and a Yamaguch type finiteness theorem in Finser geometry.

We present methods to construct interesting surfaces of general type via $\mathbb{Q}$-Gorenstein smoothing of a singular surface obtained from an elliptic surface. By applying our methods to special Enriques surfaces, we construct new examples of a minimal surface of general type with $p_g=0$, $π_1=\mathbb{Z}/2\mathbb{…