arXiv subjects
Publications and source records attributed to Ivan Yudin.
Each self-similar dendrite K with a finite self-similar boundary defines a finite acyclic edge-labeled bipartite graph G, called the sprout of K. The paper shows that the sprout G determines the combinatorial properties of the dendrite K and its topological structure.
We prove that for any self-affine dendrite K generated by a polygonal system, there are constants C>0 and $\lambda\in(0, 1)$ such that for any x, y in K, the Jordan arc $\gamma$ in K with endpoints x, y satisfies the inequality $diam({\gamma})\le C |x-y|^\lambda$.
We introduce the Darboux-Lie derivative for fiber-bundle maps from natural bundles to associated fiber bundles and study its properties.
In the present paper we compute the Jacobian group of $Δ$-graph $Δ(n; k, l, m).$ The notion of $Δ$-graph continues the list of families of $I$-, $Y$- and $H$-graphs well-known in the graph theory. In particular, graph $Δ(n; 1, 1, 1)$ is isomorphic to discrete torus $C_3\times C_n.$ It this case, the structure of the Jacobian group will be find explicitly.
We show that every compact aspherical Sasakian manifold with nilpotent fundamental group is diffeomorphic to a Heisenberg nilmanifold.
We study a natural class of LCK manifolds that we call integrable LCK manifolds: those where the anti-Lee form $η$ corresponds to an integrable distribution. As an application we obtain a characterization of unimodular integrable LCK Lie algebras as Kähler Lie algebras equipped with suitable derivations.
It is important for applications of Homological Algebra in Representation Theory to have control over the behaviour of (minimal) projective resolutions under various functors. In this article we describe three broad families of functors that preserve such resolutions. We will use these results in our work on Representation Theory of Schur algebras.
In our previous work arXiv:1306.1770, we found all Borel-Schur algebra of finite representation type. In the present article, we determine which Borel-Schur algebras of infinite representation type are tame, and which are wild.
We provide models that are as close as possible to being formal for a large class of compact manifolds that admit a transversely Kaehler structure, including Vaisman and quasi-Sasakian manifolds. As an application we are able to classify the corresponding nilmanifolds.
We provide a new, self-contained and more conceptual proof of the result that an almost contact metric manifold of dimension greater than 5 is Sasakian if and only if it is nearly Sasakian.
Experiments were performed with Fabry-Perot optical resonators in vacuum at low temperatures. Mirrors were applied on substrates of various optical materials. The infrared laser with a wavelength of 1.064 microns was used. The pump power at the maximum could reach 450 mW. The evolution of the optical properties of the FP cavity was traced in the temperature range (300 - 10)K. The main parameters measured were the integral characteristics of the FP resonances: sharpness (finesse) and contrast of interference. Three types of substrates were tested: a sitall -- the optical glass with ultra low thermal expansion (ULE), sapphire and calcium fluoride. During cooling, the degradation of the integral characteristics of the FP cavity was observed for the sitall mirrors due to the loss of the properties of (ULE), for sapphire mirrors due to the birefringence effect. The satisfactory constancy of the integral characteristics of the FP resonator on calcium fluoride was demonstrated in the entire temperature range studied 1
We prove that every nearly Sasakian manifold of dimension greater than five is Sasakian. This provides a new criterion for an almost contact metric manifold to be Sasakian. Moreover, we classify nearly cosymplectic manifolds of dimension greater than five.
We show how decreasing diagrams introduced in the theory of rewriting systems can be used to prove coherence type theorems in category theory. We apply this method to describe a coherent presentation of the $0$-Hecke monoid $\mathcal{H}(Σ_n)$ of the symmetric group $Σ_n$, i.e. a presentation by generators, relations, and relations between relations.
We establish a Hard Lefschetz Theorem for the de Rham cohomology of compact Vaisman manifolds. A similar result is proved for the basic cohomology with respect to the Lee vector field. Motivated by these results, we introduce the notions of a Lefschetz and of a basic Lefschetz locally conformal symplectic (l.c.s.) manifold of the first kind. We prove that the two notions are equivalent if there exists a Riemannian metric such that the Lee vector field is unitary and parallel and its metric dual $1$-form coincides with the Lee $1$-form. Finally, we discuss several examples of compact l.c.s. manifolds of the first kind which do not admit compatible Vaisman metrics.
We construct an action of the Hecke monoid on the category of rational modules for the quantum negative Borel subgroup of the quantum general linear group. We also show that this action restricts to the category of polynomial modules for this quantum subgroup and induces an action on the category of modules for quantised Borel-Schur algebras.
We find a family of five dimensional completely solvable compact manifolds that constitute the first examples of $K$-contact manifolds which satisfy the Hard Lefschetz Theorem and have a model of Tievsky type just as Sasakian manifolds but do not admit any Sasakian structure.
In this paper we prove a useful formula for the graded commutator of the Hodge codifferential with the left wedge multiplication by a fixed $p$-form acting on the de Rham algebra of a Riemannian manifold. Our formula generalizes a formula stated by Samuel I. Goldberg for the case of 1-forms. As first examples of application we obtain new identities on locally conformally Kaehler manifolds and quasi-Sasakian manifolds. Moreover, we prove that under suitable conditions a certain subalgebra of differential forms in a compact manifold is quasi-isomorphic as a CDGA to the full de Rham algebra.
We provide a general method to construct examples of quasi-Sasakian 3-structures on a (4n+3)-dimensional manifold. Moreover, among this class, we give the first explicit example of a compact 3-quasi-Sasakian manifold which is not the global product of a 3-Sasakian manifold and a hyper-Kähler manifold.