Solves a specific question in mapping class group theory.
problem A specific question in mapping class group theory.
method Analyzes a paper by Etnyre and Van Horn-Morris.
result Answers a specific question in mapping class group theory.
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48 results for “Van Horn-Morris”
Affirmative answer to a question about symmetric mapping classes and positive factorizations.
problem Whether a symmetric mapping class admitting a positive factorization is a lift of a quasi-positive braid.
method Investigated a specific question from a previous paper, answered affirmatively under certain conditions.
result Affirmative answer to the question for mapping classes satisfying certain cyclic conditions.
New method shows some 3D shapes can't be filled in certain ways.
problem Obstructing Liouville and weak fillability of contact structures.
method Introducing a new method to obstruct fillability.
result Various rational homology 3-spheres admit strongly fillable contact structures without Liouville fillings.
Study shows bounds on symplectic fillings for spinal open book decompositions.
problem Understanding symplectic fillings of contact 3-manifolds.
method Introduced spine removal surgery operation to prove universal bounds.
result Proves a universal bound on the Euler characteristic and signature of minimal symplectic fillings.
In the present paper we describe compatible open books for the fibre connected sum along binding components of open books, as well as for the fibre connected sum along multi-sections of open books. As an application the first description provides simple ways of constructing open books supporting all tight contact struc…
By recent results of Baker--Etnyre--Van Horn-Morris, a rational open book decomposition defines a compatible contact structure. We show that the Heegaard Floer contact invariant of such a contact structure can be computed in terms of the knot Floer homology of its (rationally null-homologous) binding. We then use this …
On a compact oriented surface of genus with boundary components, , we consider positive factorizations of the boundary multitwist , where is the positive Dehn twist about the boundary . We prove that for , the boundary multitwis…
Classification of fillings for a specific type of contact surgery on the Hopf link.
problem Classifying the minimal symplectic fillings of a specific type of contact surgery on the Hopf link.
method Performed contact (-1)-surgery on a Legendrian representative of the Hopf link, classified the minimal symplectic fillings up to homeomorphism.
result Extended the classification of fillings to a broader range of structures, including those not universally tight.
Extends spectral order definition to contact manifolds with convex boundary.
problem Defining spectral order for contact manifolds with convex boundary.
method Extends Heegaard Floer homology definition and proves bounds on contact structures.
result Establishes bounds on contact structures and spectral order.
A two-dimensional open book (S,h) determines a closed, oriented three-manifold Y(S,h) and a contact structure C(S,h) on Y(S,h). The contact structure C(S,h) is Stein fillable if h is positive, i.e. h can be written as a product of right-handed Dehn twists. Work of Wendl implies that when S has genus zero the converse s…
In this paper we show that to each planar line arrangement defined over the real numbers, for which no two lines are parallel, one can write down a corresponding relation on Dehn twists that can be read off from the combinatorics and relative locations of intersections. This leads to an alternate proof of Wajnryb's gen…
Revisits Van Est theory for Lie groupoids using homotopy inverses.
problem Relating Lie groupoids and their Lie algebroids cohomology.
method Using the Perturbation Lemma from homological algebra to construct homotopy inverses.
result Constructs homotopy inverses to the van Est differentiation maps at the cochain level.
Match van Stockum dust to vacuum metrics with a single parameter.
problem Matching van Stockum dust to vacuum metrics.
method 1-parametric family of non-static Papapetrou vacuum metrics, Ehlers and Kramer--Neugebauer transformations.
result Explicit examples of matching, including Bonnor metric and Lanczos--van Stockum dust metric.
The Van Est homomorphism for a Lie groupoid , as introduced by Weinstein-Xu, is a cochain map from the complex of groupoid cochains to the Chevalley-Eilenberg complex of the Lie algebroid of . It was generalized by Weinstein, Mehta, and Abad-Crainic to a morphism from…
New theorem shows embedding restrictions for manifold skeletons.
problem Embedding restrictions for triangulated manifolds.
method Proves van Kampen-Flores theorem for manifolds with specific Stiefel-Whitney classes.
result Triangulated manifolds with non-trivial Stiefel-Whitney classes cannot embed into .
Simple ML models generate art completions.
problem Creating art through machine learning.
method Single-output classification and regression models trained on various image datasets.
result Generated images complete missing parts of input images.
Direct proofs of implications between three theorems on maps of simplex.
problem Understanding relations between three theorems on maps of simplex.
method Direct proofs using interesting relations between van Kampen and Conway-Gordon-Sachs numbers.
result Exhibited relations and direct proofs of implications between the theorems.
Comment on "Solving Statistical Mechanics Using VANs": Introducing saVANt - VANs Enhanced by Importance and MCMC Samplingcond-mat.stat-mech
Enhances statistical mechanics solving using VANs with MCMC or importance sampling.
problem Sampling error in solving statistical mechanics using VANs.
method Integrates MCMC or importance sampling to correct sampling error in VANs.
result Asymptotically unbiased estimators for physical quantities are achieved.
The paper refines cohomology of VB-groupoids with homogeneous cochains.
problem Cohomology of VB-groupoids with linear structure.
method Refine cohomology by considering k-homogeneous cochains.
result Van Est theorem for k-homogeneous cochains on VB-groupoids.
VAN method optimizes learning tasks with unified methods.
problem Optimizing learning tasks in active and reinforcement learning.
method Variational Adaptive-Newton method that unifies optimization, inference, and evolution strategies.
result VAN performs well on various learning tasks.
Analyses cohomology relations for moving frames and coframes.
problem Relating Hopf cyclic cohomology of moving frames and coframes.
method Uses van Est analogy for DG Hopf algebras.
result Establishes cohomology isomorphism for DG Hopf algebras.
The paper derives Gauss-Bonnet theorems for deformed connections in affine and rigid motions groups.
problem Computing curvature and geodesic curvature for surfaces and curves in affine and rigid motions groups.
method Defined deformed Schouten-Van Kampen connections, computed Gaussian curvature limits, and signed geodesic curvature.
result Derived Gauss-Bonnet theorems for deformed connections in affine and rigid motions groups.
Graphs from van der Corput sequence embed into Chamanara surface.
problem Embedding graphs from van der Corput sequence into surfaces.
method Constructed -regular graphs from van der Corput sequence and Kronecker sequence, embedded into torus and Chamanara surface.
result Graphs from van der Corput sequence embed into Chamanara surface with one edge removal.
Generalizes van Est map to sheaves of sections taking values in -modules.
problem Classifying geometric structures involving Lie groupoids and stacks.
method Infinitesimal description of -modules and generalized van Est map.
result Definition and study of the generalized van Est map.
Study finds multiple solutions for Van der Waals-Cahn-Hilliard equation on manifolds.
problem Finding multiple solutions for a specific equation on manifolds.
method Combines Lusternik-Schnirelman and Morse theory with a photography method.
result Establishes multiplicity of solutions using topological invariants.
Generalizes van Est map to geometric stacks and homotopy theory.
problem Computing cohomology of geometric stacks and Lie algebroids.
method Generalizes van Est map to stacks and foliations, using modules instead of representations.
result Derives new cohomology results and unifies differentiable stacks, Lie algebroids, and homotopy theory.
On the embeddability of math.GT
Embeddability of simplicial complex linked to 's embeddability.
problem Relating embeddability of to 's embeddability.
method Comparing embeddability conditions for and .
result Embeddability of equivalent to vanishing van Kampen obstruction for .
Maps Lie 2-groups to Weil algebras, showing cohomology isomorphisms.
problem Cohomology of strict Lie 2-groups.
method Constructs van Est map using double complex and Weil algebra.
result Induces isomorphisms in cohomology under connectedness.
Statistical Mechanics Calculations Using Variational Autoregressive Networks and Quantum Annealingcond-mat.dis-nn
New method uses quantum annealing and VAN for better statistical mechanics calculations.
problem Difficulty in computing partition function in statistical mechanics.
method Combines quantum annealing samples with variational autoregressive networks.
result Enhanced accuracy in finite-size Sherrington-Kirkpatrick model.
A cubic identity for the Infeld-van der Waerden field is found and its application to verifying an explicit formula for the spinor components of the metric connection is demonstrated.
We generalize C. Van Cott's results on the and -invariants of cabled knots to apply to general satellite knots. This paper uses no Heegaard-Floer homology, relying on more geometric techniques.
Study finds multiple solutions to a complex equation with volume constraint.
problem Finding multiple solutions to a nonlinear elliptic equation with a specific potential.
method Analyzes a Van der Waals-Allen-Cahn-Hilliard equation with a linear volume constraint on a bounded Lipschitz domain.
result Estimates the number of solutions using topological and homological invariants.
This paper belongs to a series devoted to the study of the cohomology of classifying spaces. Generalizing the Weil algebra of a Lie algebra and Kalkman's BRST model, here we introduce the Weil algebra associated to any Lie algebroid . We then show that this Weil algebra is related to the Bott-Shulman-Stasheff…
Groupoids help define Riemann sums on manifolds.
problem Defining Riemann sums on compact manifolds.
method Using groupoids and the van Est map.
result Riemann sums converge to the usual integral.
The Schouten-van Kampen affine connection adapted to an almost (para) contact metric structuremath.DG
We study the Schouten-van Kampen connection associated to an almost contact or paracontact metric structure. With the help of such a connection, some classes of almost (para) contact metric manifolds are characterized. Certain curvature properties of this connection are found.
New connections defined for a specific geometric structure.
problem Characterizing manifolds with a paracontact structure.
method Introduced and studied a pair of associated Schouten-van Kampen affine connections.
result Curvature properties of the connections are obtained.
Lie algebra cohomology reformulated in a topological framework.
problem Classical Lie algebra cohomology results.
method Topological reformulation of Lie algebra cohomology.
result Shapiro lemma and van Est isomorphism generalize to topological setting.
Survey on approximability of graph embeddings and related problems.
problem Determining when graphs can be embedded in the plane without intersections.
method Criteria for approximability by embeddings and van Kampen obstruction.
result Completeness of the van Kampen obstruction for approximability by embeddings.
The paper calculates curvature limits and Gauss-Bonnet theorems in the Heisenberg group.
problem Computing curvature limits and Gauss-Bonnet theorems in the Heisenberg group.
method Sub-Riemannian limits of Gaussian curvature, Schouten-Van Kampen affine connections, and adapted connections.
result Gauss-Bonnet theorems associated with Schouten-Van Kampen affine connections in the Heisenberg group.
Proves integrability of strict Lie 2-algebras using cohomological methods.
problem Integrability of strict Lie 2-algebras.
method Van Est theorems relating cohomologies of Lie 2-groups and algebras.
result Proves integrability of Lie 2-algebras.
In the first section we discuss Morita invariance of differentiable/algebroid cohomology. In the second section we present an extension of the van Est isomorphism to groupoids. This immediately implies a version of Haefliger's conjecture for differentiable cohomology. As a first application we clarify the connection be…
Paper derives closed-form solutions for CEV model using semiclassical approximation.
problem Analyzing the constant elasticity variance (CEV) option pricing model.
method Utilizes semiclassical (WKB) approximation and Van Vleck-Morette determinant.
result Derives an exponential factor not previously considered in the kernel.
Researchers define and evaluate quasi-local mass near axially symmetric null infinity.
problem Defining and evaluating quasi-local mass at null infinity.
method Using Bondi-van der Burg-Metzner coordinates, the researchers evaluate the Wang-Yau quasilocal mass on surfaces of unit size at null infinity of axi-symmetric spacetimes.
result Evaluation of quasi-local mass near axially symmetric null infinity.
Paper calculates homotopy types of non-compact surfaces using groupoids.
problem Computing homotopy types of non-compact foliated surfaces.
method Application of van Kampen theorem for groupoids.
result Computation of homotopy types for specific non-compact surfaces.
Pair of associated Schouten-van Kampen connections adapted to an almost contact B-metric structuremath.DG
There are introduced and studied a pair of associated Schouten-van Kampen affine connections adapted to the contact distribution and an almost contact B-metric structure generated by the pair of associated B-metrics and their Levi-Civita connections. By means of the constructed non-symmetric connections, the basic clas…
Computes knot groups for torus links using Seifert-van Kampen theorem.
problem Computing knot groups for torus links.
method Groupoid version of the Seifert-van Kampen theorem.
result Economical presentations of knot groups for torus links.
Study hypoelliptic operators on Carnot manifolds, extending index theory results.
problem Index theory of hypoelliptic operators on Carnot manifolds.
method Operator K-theory and geometric K-homology.
result Compute Fredholm index of hypoelliptic operators on Carnot manifolds.
Proves generic nondegeneracy for solutions under volume constraint in closed manifolds.
problem Proving nondegeneracy for solutions of the Van der Waals-Allen-Cahn-Hilliard equation.
method Adapting techniques from previous research to prove nondegeneracy.
result Generic nondegeneracy for solutions of the Van der Waals-Allen-Cahn-Hilliard equation under a volume constraint in closed manifolds.