arXiv research

We continue here the investigation of the relationship between the intersection of a pair of subgroups of a Kleinian group, and in particular the limit set of that intersection, and the intersection of the limit sets of the subgroups. Of specific interest is the extent to which the intersection of the limit sets being …

Max arcs on spheres intersecting twice, proven.

We prove that on a punctured oriented surface with Euler characteristic chi < 0, the maximal cardinality of a set of essential simple arcs that are pairwise non-homotopic and intersecting at most once is 2|chi|(|chi|+1). This gives a cubic estimate in |chi| for a set of curves pairwise intersecting at most once on a cl…

Study on shortest geodesics with self-intersections on hyperbolic surfaces.

Extended Birman-Series result to geodesics with infinitely many self-intersections.

The paper extends the avoidance principle for mean curvature flows, proving new intersection dimension monotonicity results.

Sharp lower bound on fold singularities self-intersections.

Generalizes intersection product for PL pseudomanifolds, proving duality.

A method to compute intersection numbers with matrices of positive corank.

Study on symmetry defects of complete intersections in complex space.

Study properties of self-similar continua with finite intersection property.

New theorems link graph properties to metric space dimensions.

Let X be a pseudomanifold. In this text, we use a simplicial blow-up to define a cochain complex whose cohomology with coefficients in a field, is isomorphic to the intersection cohomology of X, introduced by M. Goresky and R. MacPherson. We do it simplicially in the setting of a filtered version of face sets, also cal…

Corrects a mistake in a theorem about hyperbolic groups.

The paper explores intersectional fairness in machine learning, proving bounds on it.

Paper certifies intersection of minimum-volume confidence sets for multinomial outcomes.

Geodesics with bounded angles have zero Hausdorff dimension.

Study of intersections in Hamiltonian orbits on cotangent bundles.

Study on geodesics proving index and intersection bounds, with examples of multiplicity.

Study on intersection norms and disk complements of curves on surfaces.

Proves curves on surfaces intersect at most once, matching known constructions.

Proves rigidity of homeomorphisms for lamination spaces.

Study intersection polynomials of long virtual knots with supporting genera.

Holomorphic foliations on complex manifolds without invariant complete intersections.

Study intersection homotopy groups in coarsenings of CS sets.

Interprets SL3-web intersections on surfaces.

Paper explores topological invariance in torsion-sensitive intersection homology.

Consider a transitive action of a Lie group $G$ on a (real analytic) manifold $M$ of dimension $m$, and two (embedded) submanifolds $A$ and $B$ in $M$ of sufficiently large class and of dimension $k$ and $l$, respectively. We prove that, for a generic $σ\in G$, the intersection $σ(A) \cap B$ is transversal, whence a su…

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

Study on curves on surfaces with bounds on intersections.

Study on shortest geodesics crossing multiple times on hyperbolic surfaces with cusps.

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…

Proves intersection properties of minimal hypersurfaces in various spaces.

I answer an open question left by Gui-Song Li in "On self-intersections of immersed surfaces" (AMS Proceedings, Volume 126, 1998, pp.3721-3726.) The intersection graph $M(i)$ of a generic surface $i:F \to S^3$ is the set of values which are either singularities or intersections. It is a multigraph whose edges are trans…

Minimal number of caps covering an n-sphere is n+2.

The paper calculates 4-manifold properties from a trisection diagram.

Two flat sub-Lorentzian problems on Martinet distribution differ in attainable set intersections.

Several authors have recently attempted to show that the intersection of three simply connected subcontinua of the plane is simply connected provided it is non-empty and the intersection of each two of the continua is path connected. In this note we give a very short complete proof of this fact. We also confirm a relat…

New bounds on curves on torus with few intersections.

Algorithm corrects bias in classification data.

We show that the adjacency matrices of the intersection graphs of chord diagrams satisfy the 2-term relations of Bar-Natan and Garoufalides [bg], and hence give rise to weight systems. Among these weight systems are those associated with the Conway and HOMFLYPT polynomials. We extend these ideas to looking at a space o…

The first part of this paper exposits a simple geometric description of the Kirby-Siebenmann invariant of a 4--manifold in terms of a quadratic refinement of its intersection form. This is the first in a sequence of higher-order intersection invariants of Whitney towers studied by the authors, particularly for the 4--b…

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

A new method clusters intersecting lines using hypergraphs.

The study limits intersections of curves on a torus.

The study bounds the number of non-intersecting loops on a surface.

Solves Plateau's problem for curves with self-intersections.

Alesker has introduced the space $\mathcal V^\infty(M)$ of {\it smooth valuations} on a smooth manifold $M$, and shown that it admits a natural commutative multiplication. Although Alesker's original construction is highly technical, from a moral perspective this product is simply an artifact of the operation of inters…