arXiv research

Article proves tangent complex structure of Lie n-groupoid.

The decorated hypercube found in the construction of Khovanov homology for links is an example of a Boolean lattice equipped with a presheaf of modules. One can place this in a wider setting as an example of a coloured poset, that is to say a poset with a unique maximal element equipped with a presheaf of modules. In t…

Khovanov homology for pro-tangles and spectral sequences

In this article we give an equivariant version for the construction of generic models on presheaves of structures. We deal with first order structures endowed with a suitable action of some fixed group, say $G$; we call them $G$-structures. We show that every exact presheaf of $G$-structures $\mathcal{M}$ has a generic…

Paper proves model structures equal for smooth manifolds and Cartesian spaces.

Develops a new exponential map for time-varying vector fields.

The procedure "Lie group --> Lie algebra" has a generalization "simplicial manifold --> L_infinity algebra", or yet better, "presheaf on the category of surjective submersions --> L_infinity algebra". We describe this generalization, together with its higher-order extensions.

We introduce notions such as cdp presheaf, cds precosheaf, Mayer-Vietoris system, and investigate their properties. As applications, we study cohomologies with values in local systems on smooth manifolds and Dolbeault cohomologies with values in locally free sheaves on complex manifolds, where the compactness is not ne…

We introduce the notion of a positive opetope and positive opetopic cardinals as certain finite combinatorial structures. The positive opetopic cardinals to positive-to-one polygraphs are like simple graphs to free omega-categories over omega-graphs, c.f. [MZ]. In particular, they allow us to give an explicit combinato…

New smooth models for string groups defined in ∞-categories.

Detecting exotic spheres involves analyzing framed configuration spaces.

In this paper we introduce $B_{α,β}^{k}$-manifolds as generalizations of the notion of smooth manifolds with $G$-structure or with $k$-bounded geometry. These are $C^{k}$-manifolds whose transition functions $\varphi_{ji}=\varphi_{j}\circ\varphi_{i}^{-1}$ are such that $\partial^μ\varphi_{ji}\in B_{α(r)}\cap C^{k-β(r)}…

In this paper we consider existence and multiplicity results concerning affine connections on $C^{k}$-manifolds $M$ whose coefficients are as regular as one needs, following the regularity theory introduced in arXiv:1908.04442. We show that if $M$ admits a $B_{α,β}^{k}$-structure, then the existence of such regular con…

An automorphism on a complex supermanifold $\mathcal M$ is called unipotent if it reduces to the identity on the associated graded supermanifold $gr(\mathcal M)$. These automorphisms are close to be complementary to those responsible for homogeneity of a supermanifold. In analogy, their study yields results on the clas…

New skein categories for non-semisimple settings, extending existing theory.

New method recovers differential cohomology from diffeological spaces.

We construct non-constructible simplicial $d$-spheres with $d+10$ vertices and non-constructible, non-realizable simplicial $d$-balls with $d+9$ vertices for $d\geq 3$.

A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system(RIFS) with function scaling factors and estimate their box-counting dimension. Then we present a method of construction of wider class of fractal su…

Modified curve shortening flow constructs $λ$-Angenent curve.

Article constructs coassociative submanifolds in Joyce's $G_2$-manifolds.

The twist construction is a geometric model of T-duality that includes constructions of nilmanifolds from tori. This paper shows how one-dimensional foliations on manifolds may be used in a shear construction, which in algebraic form builds certain solvable Lie groups from Abelian ones. We discuss other examples of geo…

We describe various constructions in Sasakian geometry. First we generalize the join construction of the first two authors to arbitrary Sasakian manifolds. We then give several examples, including ones which prove the existence of Sasakian-Einstein metrics on manifolds homeomorphic to $S^2\times S^5.$ Then we use a gen…

Recently, there has been emerging interest in constructing reproducing kernel Banach spaces (RKBS) for applied and theoretical purposes such as machine learning, sampling reconstruction, sparse approximation and functional analysis. Existing constructions include the reflexive RKBS via a bilinear form, the semi-inner-p…

We construct bi-invariant total orderings of residually torsion-free nilpotent groups by using Chen's iterated integrals. This construction can be seen as a generalization of the Magnus ordering of the free groups, and equivalent to the classical construction which uses an iteration of central extensions. Our geometric…

The paper constructs infinitely many surfaces with specific mean curvature.

Explains a 1978 construction for Yang-Mills instantons.

We construct several non-trivial examples of CAT(1) spaces by using the idea of free construction.

We study the performance of the adaptive construction scheme for a Bayesian inference on the Quadratic GARCH model which introduces the asymmetry in time series dynamics. In the adaptive construction scheme a proposal density in the Metropolis-Hastings algorithm is constructed adaptively by changing the parameters of t…

New pseudomodular groups constructed from jigsaw construction.

Study constructs associative submanifolds in $G_2$-manifolds from orbifolds.

Survey on rigorous construction of supersymmetric path integral.

Test-asset construction affects factor model performance.

We introduce the cutting construction of possibly non-compact symplectic toric manifolds, in particular, toric symplectic cones that correspond to a weakly convex good cone. Since the symplectization of a toric contact manifold is a toric symplectic cone, we can also construct toric contact manifolds that correspond to…

Extends knot surgery to exotic four-manifolds.

We construct calibrated submanifolds of R^7 and R^8 by viewing them as total spaces of vector bundles and taking appropriate sub-bundles which are naturally defined using certain surfaces in R^4. We construct examples of associative and coassociative submanifolds of R^7 and of Cayley submanifolds of R^8. This construct…

Researchers match complex affine structures in mirror constructions.

The paper constructs solutions to a critical Dirac equation on spheres.

In this paper, we construct the index bundle gerbe of a family of self-adjoint Dirac-type operators, refining a construction of Segal. In a special case, we construct a geometric bundle gerbe called the caloron bundle gerbe, which comes with a natural connection and curving, and show that it is isomorphic to the analyt…

Two constructions link path geometries to almost Grassmann structures.

Constructs subvarieties in translation surface strata using combinatorial input.

Springer varieties appear in both geometric representation theory and knot theory. Motivated by knot theory and categorification Khovanov provides a topological construction of $(n/2, n/2)$ Springer varieties. We extend Khovanov's construction to all two-row Springer varieties. Using the combinatorial and diagrammatic …

Constructs harmonic maps between special geometric shapes.

This is the second paper in a series of papers aimed at providing a geometric construction of modular functors and topological quantum field theories from conformal field theory building on the constructions in [TUY] and [KNTY]. We give a geometric construct of a modular functor for any simple Lie-algebra and any level…

We give an algebro-geometric construction of some of the non-arithmetic ball quotients constructed by the author, Parker and Paupert. The new construction reveals a relationship between the corresponding orbifold fundamental groups and the automorphism group of the Klein quartic, and also with groups constructed by Bar…

We constructed physically stable sp2 negatively curved cubic carbon structures which reticulate a Schwarz P-like surface. The method for constructing such crystal structures is based on the notion of the standard realization of abstract crystal lattices. In this paper, we expound on the mathematical method to construct…

Paper proposes NNAFC for automatic financial factor construction.

The article consists of the Russian and English variants of Ph.D. Thesis in which the answers is given on the following questions: 1. how to construct the spinor formalism for n=6; 2. how to construct the spinor formalism for n=8; 3. how to prolong the Riemannian connection from the tangent bundle into the spinor one w…

Constructs surfaces with specific topologies and curvatures.