arXiv research

Paper calculates eigenvalues of a specific triangle on a sphere.

Proves the relative h-principle for SL(3,R)^2 3-forms on 6-manifolds.

New insights into $(2,3,5)$-distributions via Legendrian curves.

Maximal representations into $\mathrm{SO}_0(2,3)$ have bounded volume.

As was shown by a part of the authors, for a given $(2, 3, 5)$-distribution $D$ on a $5$-dimensional manifold $Y$, there is, locally, a Lagrangian cone structure $C$ on another $5$-dimensional manifold $X$ which consists of abnormal or singular paths of $(Y, D)$. We give a characterization of the class of Lagrangian co…

No minimal chart of type (2,3,2) exists.

We give criteria for framed links and 3-manifolds to be periodic of prime order. As applications we show that the Poincare sphere is of periodicity 2, 3, 5 only and the Brieskorn sphere (2,3,7) is of periodicity 2, 3, 7 only.

We prove that the Dolgachev surface E(1)_{2,3} admits a handlebody decomposition without 1- and 3- handles, and we draw the explicit picture of this handlebody. We also locate a "cork" inside of E(1)_{2,3}, so that E(1)_{2,3} is obtained from E(1) by twisting along this cork.

Essential triangulations of certain manifolds are connected via specific moves.

We classify multiply transitive homogeneous real (2,3,5) distributions up to local diffeomorphism equivalence.

Local equivalence shown between specific distributions and flat Cartan distribution.

Here we draw a handlebody picture for the exotic CP^2 # 3(-CP^2), constructed by Akhmedov and Park.

The paper characterizes Pfaffian embeddings from 2,3,5-manifolds to 7-dimensional isotropic spaces.

Classifies multiply-transitive (2,3,5)-distributions using modern Cartan geometry.

The paper extends radius estimates for stable hypersurfaces in 2, 3, and 4 dimensions.

Eta invariant of (2,3,5) nilmanifolds vanishes but eta function is nontrivial.

Minimal charts of specific type contain unique subgraphs.

We compute the Ozsváth--Szabó contact invariants for all tight contact structures on the manifolds -Σ(2,3,6n-1).

In this paper we construct a minimal symplectic 4-manifold and prove it is homeomorphic but not diffeomorphic to CP^2 # 3(-CP^2)

We calculate the universal character ring of a class of two-generator, one-relator groups. As an application we give a less technical proof of a result in [LT] on the universal character ring of the (-2,3,2n+1)-pretzel knot. We also give an elementary proof of a result in [Ma] on the character variety of the (-2,3,2n+1…

The paper minimizes Borda regret in dueling bandits models.

We compute two vector field models of the Carnot algebra with the growth vector (2,3,5,8), and an infinitesimal symmetry of the corresponding sub-Riemannian structure.

If p/q > 18, p is odd, and $p/q \ne 37/2$, (p,q)-Dehn surgery for the (-2,3,7)-pretzel knot produces a 3-manifold without Reebless foliation.

This paper is an addendum to [4], in which the authors constructed a simply connected minimal complex surface of general type with p_g=0 and K^2=3. In this paper we construct a new non-simply connected minimal surface of general type with p_g=0, K^2=3 and H_1=Z/2Z using a rational blow-down surgery and Q-Gorenstein smo…

We present enumerations of a class of toroidal graphs which give rise to semi-equivelar maps. There are eleven different types of semi-equivelar maps on the torus. These are of the types $\{3^{6}\}$, $\{4^{4}\}$, $\{6^{3}\}$, $\{3^{3}, 4^{2}\}$, $\{3^{2}, 4, 3, 4\}$, $\{3, 6, 3, 6\}$, $\{3^{4}, 6\}$, $\{4, 8^{2}\}$, $\…

New representation theory for surface groups to SO0(2,3).

We study topological structures of the sets $(0,1/2)^3 \cap Ω$ and $(0,1/2)^3 \setminus Ω$, where~$Ω$ is one special algebraic surface defined by a symmetric polynomial in variables $a_1,a_2,a_3$ of degree~$12$. These problems arise in studying of general properties of degenerate singular points of dynamical systems ob…

New adaptive learning rate for FTRL reduces regret to Θ(T^2/3).

Let K_s be a (-2,3,2s+1)-type Pretzel knot (s >= 3) and E(K_s)(p/q) be a closed manifold obtained by Dehn surgery along K_s with a slope p/q. We prove that if q>0, p/q >= 4s+7 and p is odd, then E(K_s)(p/q) cannot contain an R-covered foliation. This result is an extended theorem of a part of works of Jinha Jun for (-2…

For the link $M$ of a normal complex surface singularity $(X,0)$ we ask when a knot $K\subset M$ exists for which the answer to whether $K$ is the link of the zero set of some analytic germ $(X,0)\to (\mathbb C,0)$ affects the analytic structure on $(X,0)$. We show that if $M$ is an integral homology sphere then such a…

In the present paper, we will show that a $(p,q,r)$-pretzel knot has the representativity 3 if and only if $(p,q,r)$ is either $\pm(-2,3,3)$ or $\pm(-2,3,5)$. We also show that a large algebraic knot has the representativity less than or equal to 3.

The study generalizes a specific geometric correspondence to higher dimensions.

Harer-Kas-Kirby conjectured that every handle decomposition of the elliptic surface E(1)_{2,3} requires both 1- and 3-handles. We prove that the elliptic surface E(n)_{p,q} has a handle decomposition without 1-handles for $n\geq 1$ and (p,q)=(2,3),(2,5),(3,4),(4,5).

Compactifies a component by studying metric degeneration.

Study of polynomial almost-complex curves in a specific space.

Smooth contact mappings in a flat (2,3,5)-distribution are shown to be smoother.

We analyze the classic problem of existence of Einstein metrics in a given conformal structure for the class of conformal structures inducedf Nurowski's construction by (oriented) (2,3,5) distributions. We characterize in two ways such conformal structures that admit an almost Einstein scale: First, they are precisely …

We calculate the twisted Alexander polynomials of $(-2,3,2n+1)$-pretzel knots associated to their holonomy representations. As a corollary, we obtain new supporting evidences of Dunfield, Friedl and Jackson's conjecture, that is, the twisted Alexander polynomials of hyperbolic knots associated to their holonomy represe…

We compute the algebraic equation of the universal family over the Kenyon-Smillie $(2,3,4)$-Teichmüller curve and give a nice geometric description of the torsion map. Moreover, we re-prove independently that the found algebraic equation describes a Teichmüller curve by computing the Picard-Fuchs equation associated to…

Motivated by Stipsicz and Szabó's exotic 4-manifolds with b_2^+=3 and b_2^-=8, we construct a family of simply connected smooth 4-manifolds with b_2^+=3 and b_2^-=8. As a corollary, we conclude that the topological 4-manifold 3{CP}^2#8{-CP}^2 admits infinitely many distinct smooth structures.

The paper defines a new equivalence relation for knot projections and finds an infinite number of distinct classes.

In this paper we study the (equivariant) topological types of a class of 3-dimensional closed manifolds (i.e., 3-dimensional small covers), each of which admits a locally standard $(\mathbb{Z}_2)^3$-action such that its orbit space is a simple convex 3-polytope. We introduce six equivariant operations on 3-dimensional …

We study arithmetic properties of the growth rates of cofinite 3-dimensional hyperbolic Coxeter groups whose dihedral angles are of the form $\fracπ{m}$ for $m=2,3,4,5,6$ and show that the growth rates are always Perron numbers.

The paper constructs paths of SL2(R) representations for pretzel knots and shows left-orderability conditions.

Improved single-pass streaming MAB regret bound to O(K^1/3T^2/3).

Flat isometric immersions in 3D are developable if they are $C^{1,2/3}$ regular.

We construct a 1-parameter family of $\mathrm{SL}_2(\mathbf{R})$ representations of the pretzel knot $P(-2,3,7)$. As a consequence, we conclude that Dehn surgeries on this knot are left-orderable for all rational surgery slopes less than 6. Furthermore, we discuss a family of knots and exhibit similar orderability resu…

In this paper, we prove that the fundamental group of the manifold obtained by Dehn surgery along a $(-2,3,2s+1)$-pretzel knot ($s\ge 3$) with slope $\frac{p}{q}$ is not left orderable if $\frac{p}{q}\ge 2s+3$, and that it is left orderable if $\frac{p}{q}$ is in a neighborhood of zero depending on $s$.