arXiv research

Mapping class group subgroups yield quasi-isometric curve complex.

Complex captures group properties, invariant under quasi-isometry.

The paper extends group constructions to coset geometries, creating new ways to combine geometries.

The study of double coset growth in specific groups confirms a conjecture about generic 3-manifolds.

We construct unitary modular categories for a general class of coset conformal field theories based on our previous study of these theories in the algebraic quantum field theory framework using subfactor theory. We also consider the calculations of the corresponding 3-manifold invariants. It is shown that under certain…

Develops intrinsic curved cosets for Cartan geometries.

For every finite graph $Γ$, we define a simplicial complex associated to the outer automorphism group of the RAAG $A_Γ$. These complexes are defined as coset complexes of parabolic subgroups of $Out^0(A_Γ)$ and interpolate between Tits buildings and free factor complexes. We show that each of these complexes is homotop…

Solves double coset problem for braid group H_n.

Geometric methods show cosets of mapping class groups for 3-manifolds.

New methods convert complex link presentations to simpler, recognizable forms.

We prove that the Cayley graph and the coset geometry of the von Dyck group $D(a,b,c)$ are linked by a vertex-to-edge duality.

Neural program embedding can be helpful in analyzing large software, a task that is challenging for traditional logic-based program analyses due to their limited scalability. A key focus of recent machine-learning advances in this area is on modeling program semantics instead of just syntax. Unfortunately evaluating su…

Paper explores link and plat presentations, showing equivalence under bridge isotopy.

In this paper, we formulate a construction of ideal coset invariants for surface-links in $4$-space using invariants for knots and links in $3$-space. We apply the construction to the Kauffman bracket polynomial invariant and obtain an invariant for surface-links called the Kauffman bracket ideal coset invariant of sur…

Proves cosets of certain subgroups in hyperbolic 3-manifold groups are conjugacy distinguished.

The Cayley graph of quandles reveals structural properties and is studied for various classes.

Study local wild mapping class groups for irregular connections on complex curves.

Study shows stable graphs in Heisenberg group are essentially planes.

Paper classifies fibers of fat Riemannian submersions with non-negative curvature.

The paper finds diffeomorphic complex intersections with distinct Hodge numbers.

In this paper, we use the technique of Finslerian submersion to deduce a flag curvature formula for homogeneous Finsler spaces. Based on this formula, we give a complete classification of even-dimensional smooth coset spaces $G/H$ admitting $G$-invariant Finsler metrics with positive flag curvature. It turns out that t…

Strong bolicity helps prove Baum-Connes conjecture for certain hyperbolic groups.

Positivity of intersections in 4-manifolds leads to taming symplectic structures.

Let M = H^3 / Γbe a hyperbolic 3-manifold of finite volume. We show that if H and K are abelian subgroups of Γand g is in Γ, then the double coset HgK is separable in Γ. As a consequence we prove that if M is a closed, orientable, Haken 3-manifold and the fundamental group of every hyperbolic piece of the torus decompo…

Condition for intersection of real flag manifolds in complex flag manifold.

In this paper, we introduce the flag-wise positively curved condition for Finsler spaces (the (FP) Condition), which means that in each tangent plane, we can find a flag pole in this plane such that the corresponding flag has positive flag curvature. Applying the Killing navigation technique, we find a list of compact …

Let M be a connected compact pseudoRiemannian manifold acted upon topologically transitively and isometrically by a connected noncompact simple Lie group G. If m_0, n_0 are the dimensions of the maximal lightlike subspaces tangent to M and G, respectively, where G carries any bi-invariant metric, then we have n_0 \leq …

Let M be a graph manifold. We prove that fundamental groups of embedded incompressible surfaces in M are separable in the fundamental group of M, and that the double cosets for crossing surfaces are also separable. We deduce that if there is a "sufficient" collection of surfaces in M, then the fundamental group of M is…

In this paper, we study normal homogeneous Finsler spaces. We first define the notion of a normal homogeneous Finsler space, using the method of isometric submersion of Finsler metrics. Then we study the geometric properties. In particular, we establish a technique to reduce the classification of normal homogeneous Fin…

Researchers calculate alpha invariant for certain complex projective spaces.

The study finds that most minimal surfaces in generic 4D manifolds intersect in complex ways.

A compact Riemannian homogeneous space $G/H$, with a bi--invariant orthogonal decomposition $\mathfrak{g}=\mathfrak{h}+\mathfrak{m}$ is called positively curved for commuting pairs, if the sectional curvature vanishes for any tangent plane in $T_{eH}(G/H)$ spanned by a linearly independent commuting pair in $\mathfrak{…

The paper characterizes and studies compact subsets of complex projective space with specific line intersection properties.

Improved bounds on shortest geodesics with self-intersections on hyperbolic surfaces.

We give the diffeomorphism classification of complete intersections with S^1-symmetry in dimension less than or equal to 6. In particular, we show that a 6-dimensional complete intersection admits a smooth non-trivial S^1-action if and only if it is diffeomorphic to the complex projective space or the quadric. We also …

3-manifold triangulation can be reconstructed from its intersection matrix.

The paper classifies differentiable structures on a line with two origins.

Study the intersection of positive closed currents using tangent currents and King's residue formula.

Let $X$ be a contractible $2$-complex which is a union of two contractible subcomplexes $Y$ and $Z.$ Is the intersection $Y\cap Z$ contractible as well? In this note, we prove that the inclusion-induced map $π_{1}(Y\cap Z)\rightarrow π_{1}(Z)$ is injective if $Y$ is $π_{1}$-injective subcomplex in a locally CAT(0) 2-co…

For a Lie group $G$ and a closed Lie subgroup $H\subset G$, it is well known that the coset space $G/H$ can be equipped with the structure of a manifold homogeneous under $G$ and that any $G$-homogeneous manifold is isomorphic to one of this kind. An interesting problem is to find an analogue of this result in the case…

In this paper, we state two combination theorems for relatively quasiconvex subgroups in a relatively hyperbolic group. Applications are given to the separability of double cosets of certain relatively quasiconvex subgroups and the existence of closed surface subgroups in relatively hyperbolic groups.

New method to compute homology and intersection form of 4-manifolds.

Constructs complete Calabi-Yau metrics from smoothed Calabi-Yau intersections.

We construct examples of $C^\infty$ smooth submanifolds in ${\Bbb C}^n$ and ${\Bbb R}^n$ of codimension 2 and 1, which intersect every complex, respectively real, analytic curve in a discrete set. The examples are realized either as compact tori or as properly imbedded Euclidean spaces, and are the graphs of quasianaly…

We show that the algebraic intersection number of Scott and Swarup for splittings of free groups coincides with the geometric intersection number for the sphere complex of the connected sum of copies of $S^2\times S^1$.

The paper consider the symmetric of Finsler spaces. We give some conditions about globally symmetric Finsler spaces. Then we prove that these spaces can be written as a coset space of Lie group with an invariant Finsler metric. Finally, we prove that such a space must be Berwaldian

We show the intersection of a compact almost complex subvariety of dimension $4$ and a compact almost complex submanifold of codimension $2$ is a $J$-holomorphic curve. This is a generalization of positivity of intersections for $J$-holomorphic curves in almost complex $4$-manifolds to higher dimensions. As an applicat…

The geometry of cosets in the subgroups H of the two-generator free group G =\textless{} a, b \textgreater{} nicely fits, via Grothendieck's dessins d'enfants, the geometry of commutation for quantum observables. Dessins stabilize point-line incidence geometries that reflect the commutation of (generalized) Pauli opera…