New structure found in loops on quasi-surfaces.
problem Understanding operations on loops in quasi-surfaces.
method Defined a quasi-Lie bialgebra structure.
result Natural operations on loops form a quasi-Lie bialgebra.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,051 papers · 148 categories
Trend · papers per month
48 results for “surface loops”
A skew loop is a closed curve without parallel tangent lines. We prove: The only complete surfaces in euclidean 3-space with a point of positive curvature and no skew loops are the quadrics. In particular, ellipsoids are the only closed surfaces without skew loops. We also prove results about skew loops on cylinders an…
Method calculates loop intersections on surfaces.
problem Computing intersections of loops on surfaces.
method Nielsen fixed point theory and Gröbner-Shirshov basis.
result Simple method to compute intersection numbers.
New method for calculating loop operations on surfaces.
problem Computing algebraic operations on loops in surfaces.
method Using fillings of surfaces by graphs to compute homological intersection number, Lie bracket, and Lie cobracket.
result Effective new approach to standard algebraic operations on loops.
Study Brownian loops on hyperbolic surfaces, linking to Selberg zeta function.
problem Understanding Brownian loops on hyperbolic surfaces and their relation to Selberg zeta function.
method Computed mass of loops and related to Selberg zeta function for geometrically finite surfaces.
result Relate total loop mass to Selberg zeta function, providing probabilistic interpretations of determinants.
Complex surfaces show non-simply connected diffeomorphism groups with non-homotopic loops.
problem Complex surfaces with non-simply connected diffeomorphism groups and non-homotopic loops.
method Exhibited examples of complex surfaces.
result Diffeomorphism groups of complex surfaces are not simply-connected and contain non-homotopic loops.
Construct minimal Lagrangian surfaces in complex projective plane via loop group method.
problem Construct minimal Lagrangian immersions from arbitrary Riemann surfaces into complex projective plane.
method Loop group method, perturbed equivariant minimal Lagrangian surfaces, Delaunay cylinders approximation.
result Construct a class of minimal Lagrangian cylinders approximating Delaunay cylinders.
The paper counts geodesic loops on surfaces without conjugate points.
problem Counting geodesic loops on surfaces of genus at least 2 without conjugate points.
method Proves asymptotic estimates for closed geodesic loops on compact surfaces with no conjugate points.
result Generalizes classical counting results and sector theorems for surfaces of strictly negative curvature.
The paper connects Riemann surface length spectra to Brownian loop measures.
problem Understanding the length spectra of Riemann surfaces with additional cusps.
method Using the Brownian loop measure to relate length spectra of Riemann surfaces with and without additional cusps.
result Expressed the total mass of Brownian loops in terms of the length of geodesic representatives.
Criteria for loop separability on surfaces using Goldman bracket.
problem Determining when two loops on an oriented surface can have disjoint representatives.
method Algebraic criteria in terms of the Goldman bracket, extended using hyperbolic geometry.
result Explicit algebraic conditions for loop separability on surfaces.
We relate the author's Lie cobracket in the module additively generated by loops on a surface with the Connes-Kreimer Lie bracket in the module additively generated by trees. To this end we introduce a pre-Lie coalgebra and a (commutative) Hopf algebra of pointed loops on a surface. In the last version I added sections…
Study on loops on non-orientable surfaces, determining cardinality and order.
problem Determining the cardinality and order of maximal complete 1-systems of loops on non-orientable surfaces.
method Proved the cardinality of maximal systems of arcs pairwise-intersecting at most once on a non-orientable surface is , and used this to determine the cardinality of maximal complete 1-systems of loops.
result Exact cardinality of maximal complete 1-systems of loops on punctured projective planes is determined.
Study finds counterexamples to simple loop conjecture in higher dimensions.
problem Simple loop conjecture for surfaces to manifolds of dimensions at least four.
method Provided specific counterexamples for every and .
result No simple loop is contained in the kernel of the map for certain surfaces and manifolds.
Study minimal Lagrangian surfaces in complex projective plane, focusing on contractible cases.
problem Construct minimal Lagrangian surfaces in complex projective plane.
method Loop group method
result Presented new classes of minimal Lagrangian surfaces.
New proof shows how to find stable loops in 3-manifolds.
problem Finding stable loops in 3-manifolds.
method Using veering triangulations and minimal stable loops.
result New proof of Mosher's Transverse Surface Theorem.
Survey on real forms of a complex equation and their connection to surface theory.
problem Describing real forms of the complex -Toda equation and their geometric implications.
method Analyzing the integrability of Maurer-Cartan forms for different real forms of loop groups.
result Each real form of corresponds to a specific surface class with integrable frames.
Minimal Lagrangian surfaces in complex hyperbolic quadric via loop group method.
problem Characterizing and constructing minimal Lagrangian surfaces in complex hyperbolic quadric.
method Loop of flat connections, isometric deformations, DPW-type representation.
result Explicit examples of minimal Lagrangian surfaces, including catenoid-type examples.
We discuss some applications of an intrinsic multipication in the space of simple loops in a surface.
A branched covering surface-knot over an oriented surface-knot is a surface-knot in the form of a branched covering over . A branched covering surface-knot over is presented by a graph called a chart on a surface diagram of . For a branched covering surface-knot, an addition of 1-handles equipped with cha…
We determine the largest (i.e. smallest index) characteristic subgroup of surface groups not containing any simple loops.
The study finds bounds on homologically independent loops on hyperelliptic hyperbolic surfaces.
problem Finding bounds on the lengths of homologically independent loops on hyperelliptic hyperbolic surfaces.
method Analyzing the genus and using constant upper bounds on minimal length of non-zero period lattice vectors.
result For any , there exists a constant such that every hyperelliptic hyperbolic surface has at least homologically independent loops of length at most .
Minimal surfaces in hyperbolic and anti-de Sitter spaces constructed using loop group methods.
problem Constructing minimal surfaces in hyperbolic and anti-de Sitter spaces.
method Loop group factorization methods.
result Minimal surfaces in hyperbolic and anti-de Sitter 3-space with -punctured sphere topology.
For any unoriented loop on a compact connected oriented surface with one boundary component, the generalized Dehn twist along the loop is defined as an automorphism of the completed group ring of the fundamental group of the surface. If the loop is simple, this is the usual right handed Dehn twist, in particular realiz…
Method computes centers of Poisson and skein algebras for loops on surfaces.
problem Computing centers of Poisson and skein algebras associated to loops on surfaces.
method Systematic method using Goldman and Wolpert's Poisson algebras and Turaev's skein algebras.
result Computed centers of various Poisson and skein algebras for finite type hyperbolic surfaces.
Study of minimal surfaces with non-trivial topology in Heisenberg group using loop group method.
problem Constructing and classifying minimal surfaces with non-trivial topology in the Heisenberg group.
method Generalized Weierstrass type representation and loop group method.
result Classification of equivariant minimal surfaces given by one-parameter subgroups.
The paper provides infinite presentations for surface groups.
problem Understanding fundamental groups of surfaces.
method Infinite presentations of fundamental groups using simple loops.
result Infinite presentations for fundamental groups of surfaces and non-orientable surfaces.
Four counterexamples in surface homology.
problem Understanding surface homology and minimal homology bases.
method Presenting four specific counterexamples.
result Minimal homology bases can be challenging to work with.
The abstract theorem is extended to higher genus surfaces.
problem Generalizing the web trace theorem to higher genus surfaces.
method Geometric derivation and spin geometry of embedded loops.
result Expansion of twisted Kasteleyn matrices for higher genus surfaces.
4-manifolds can be uniquely described as loops of Morse functions.
problem Describing 4-manifolds as loops of Morse functions.
method Proving uniqueness for each of four descriptions of 4-manifolds.
result Two loops of Morse functions yielding diffeomorphic 4-manifolds are related by specific moves.
New rays on infinite type surfaces help understand their boundaries.
problem Describe the boundary of the loop graph of infinite type surfaces.
method Combining combinatorial and geometric approaches, constructing 2-filling rays.
result Constructed the first examples of 2-filling rays on infinite type surfaces.
The theorem connects surface mapping groups to fundamental groupoids.
problem Mapping class groups of bounded surfaces.
method Proving isomorphism between mapping class groups and fundamental groupoid automorphisms.
result Mapping class groups of bounded surfaces are isomorphic to fundamental groupoid automorphisms fixing boundary loops.
Study local Weyl law on hyperbolic surfaces, identifying geodesic loops.
problem Understanding the variance of a local Weyl law on hyperbolic surfaces.
method Explicit integration of test functions, stationary phase arguments, and geometric analysis of geodesic loops.
result Identifies length-minimizing geodesic loops and sequences, proving they are simple.
Study non-orientable surfaces to find loops winding around punctures.
problem Understanding loops winding around punctures on non-orientable surfaces.
method Analyzing one-sided geodesics and their powers on non-orientable surfaces.
result Loops can wind around a puncture at most two values of for odd .
We study Wilson-'t Hooft loop operators in a class of N=2 superconformal field theories recently introduced by Gaiotto. In the case that the gauge group is a product of SU(2) groups, we classify all possible loop operators in terms of their electric and magnetic charges subject to the Dirac quantization condition. We t…
The simple loop conjecture for 3-manifolds states that every 2-sided immersion of a closed surface into a 3-manifold is either injective on fundamental groups or admits a compression. This can be viewed as a generalization of the Loop Theorem to immersed surfaces. We prove the conjecture in the case that the target 3-m…
A 2-dimensional braid over an oriented surface-knot is presented by a graph called a chart on a surface diagram of . We consider 2-dimensional braids obtained by an addition of 1-handles equipped with chart loops. We introduce moves of 1-handles with chart loops, called 1-handle moves, and we investigate how muc…
Willmore surfaces in spheres via loop groups IV: on totally isotropic Willmore two-spheres in math.DG
Totally isotropic surfaces in are not necessarily Willmore surfaces. Therefore it is the first goal of this paper to derive a geometric characterization of totally isotropic Willmore two-spheres in . This will naturally yield to a description of such surfaces in terms of the loop group language. Moreover, ap…
We prove that C. Loewner's inequality for the torus is satisfied by all hyperelliptic surfaces X, as well. We first construct the Loewner loops on the (mildly singular) companion tori, locally isometric to X away from the Weierstrass points. The loops are then transplanted to X, and surgered to obtain a Loewner loop on…
Unified representation for minimal and constant mean curvature surfaces.
problem Representing minimal and constant mean curvature surfaces in Euclidean and hyperbolic spaces.
method Integral system methods applied to Weierstrass and Bryant representations.
result Unified representation and classification of various examples.
The paper describes a new method for Willmore surfaces in spheres.
problem Finding new examples of Willmore surfaces in spheres.
method DPW approach via conformal Gauss maps.
result New examples of Willmore surfaces, including a two-sphere in .
We study manifolds with split-complex structure and apply some general results to the study of Lorentz surfaces. In particular, we apply our results to timelike minimal immersions. The conformal realization of these surfaces is obtained using a representation based on loop groups. The classical Weierstrass representati…
The study bounds the number of non-intersecting loops on a surface.
problem Bounding the number of non-intersecting loops on a surface.
method Combines probabilistic and covering space arguments, leveraging LERF property of surface groups.
result The bound matches the size of the largest known construction to within a factor of log g.
Geometric proof of curve characterization using loop-bundles.
problem Characterization of simple curves in terms of the Goldman-Turaev bracket.
method Combining combinatorial approach with geometric proof.
result Geometric proof of curve characterization conjecture.
Polynomial-time algorithm finds short non-orientable loops intersecting graph edges up to 30 times.
problem Finding short non-orientable loops intersecting graph edges efficiently.
method Combining computational biology techniques with recent graph theory results.
result Existence of short canonical non-orientable systems of loops.
In this paper, we prove homological stability of symplectomorphisms and extended hamiltonians of surfaces made discrete. We construct an isomorphism from the stable homology group of symplectomorphisms and extended Hamiltonians of surfaces to the homology of certain infinite loop spaces. We use these infinite loop spac…
Wilson loops in supersymmetric Yang-Mills theory correspond at strong coupling to extremal surfaces in . We study a class of extremal surfaces known as special Legendrian submanifolds. The "hemisphere" corresponding to the circular Wilson loop is an example of a special Legendrian submanifold, and w…
Formula proves Euler characteristic of singularized surfaces.
problem Calculating the Euler characteristic of singularized surfaces.
method Three operations: collapsing, zipping, and double loop identification.
result Formula for Euler characteristic of singularized surfaces.
Infinite diameter proved for contractible loops space.
problem Infinite diameter of contractible loops space in a compact surface.
method New functionals on normed groups, more general than quasi-morphisms.
result Proved infinite diameter of contractible loops space.