The theory of differential characters is developed completely from a de Rham - Federer viewpoint. Characters are defined as equivalence classes of special currents, called sparks, which appear naturally in the theory of singular connections. There are many different spaces of currents which yield the character groups. …
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.
169,341 papers · 148 categories
Trend · papers per month
48 results for “C) characters”
A stroke-based method reconstructs characters from noisy images.
problem Challenges in reconstructing characters from noisy images.
method Uses a weighted quadratic Bezier curve (WQBC) to represent strokes.
result Achieves excellent reconstruction in real scenes.
Character scheme of small Seifert 3-manifolds is reduced if and only if no exceptional abelian character exists.
problem Character scheme of small Seifert 3-manifolds and its reduction condition.
method Complete description of the SL2(C)-character scheme of small Seifert 3-manifolds.
result Character scheme is reduced if and only if no exceptional abelian character exists, and exceptional abelian character has multiplicity 2.
New twisted versions of wild character varieties created.
problem Constructing twisted wild character varieties.
method Creating new versions of wild character varieties.
result Twisted versions of wild character varieties constructed.
Quantum character varietiesmath.QA
Quantum character varieties unify four construction methods.
problem No specific problem stated; unification of approaches.
method Four different approaches to construction.
result Unified understanding of quantum character varieties.
We show that for any knot there exist only finitely many irreducible metabelian characters in the -character variety of the knot group, and the number is given explicitly by using the determinant of the knot. Then it turns out that for any 2-bridge knot a section of the -character va…
Study of orbifold Chern character using superconnections.
problem Chern character for orbifold settings.
method Use of flat antiholomorphic superconnections and Riemann-Roch-Grothendieck theorem.
result Uniqueness of orbifold Chern character proven.
Character varieties get a natural Poisson structure.
problem Character varieties of surfaces.
method Natural Poisson structure.
result Character varieties have a Poisson structure.
Study on deformations of trivial character in SL_2(C) for groups.
problem Deforming the trivial character in SL_2(C) for groups.
method Analyzing maps satisfying the parallelogram identity on groups and relating them to deformations of the trivial character.
result The trivial character is a smooth point if and only if H_1(G,C) has dimension less than 2.
In this paper, we give a quantum interpretation of the Bismut-Chern character form (the loop space lifting of the Chern character form) as well as the Chern character form associated to a complex vector bundle with connection over a smooth manifold in the framework of supersymmetric quantum field theories developed by …
Study shows how certain knots and tori are detected by ideal points in character varieties.
problem Detecting essential twice-punctured tori in character varieties.
method Extending Tillmann's limiting character method to new families of knots and tori.
result Explicit determination of limiting characters at ideal points for specific knots and tori.
Study SL(2,C) character schemes for finitely generated groups.
problem Characterize SL(2,C) representations of finitely generated groups.
method Define coordinate rings and equations for SL(2,C) character schemes.
result Explicit equations for character schemes of finitely presented groups.
Character variety of Borromean link solved, Alexander polynomial formula found.
problem Character variety of Borromean link
method Determined irreducible SL(2,C) character variety, found Alexander polynomial formula
result Formula for twisted Alexander polynomial on character variety
Detects essential surfaces in knots using character variety intersections.
problem Identifying essential surfaces in knot theory.
method Analyzing intersections in the character variety of hyperbolic knots.
result Intersection points in the character variety detect Seifert surfaces.
Character varieties of 2-bridge knots and links explained using Farey recursion.
problem Understanding character varieties of 2-bridge knots and links.
method Using Farey recursion to define polynomials for character varieties.
result Character varieties described in terms of polynomials defined by Farey recursion.
Computes dimensions of representation and character varieties for 2 and 3-dimensional orbifolds.
problem Computing dimensions of representation and character varieties for orbifolds.
method Analyzes varieties of representations and characters of hyperbolic and non-hyperbolic orbifolds, provides tools for computation.
result Shows that the dimension of a specific component of characters equals half the dimension of the variety of characters of the boundary.
Paper generates personalized fonts from a few characters.
problem Creating personalized fonts from a limited set of characters.
method Designs a network framework to extract and recombine character content and style using various neural networks.
result Generated characters are structurally similar to real characters.
Study character varieties for real forms of SL_n(C).
problem Characterize representations of groups in real forms of SL_n(C).
method Define and analyze G-character varieties, study involutions, and examples.
result Irreducible representations fixed by involutions are conjugate to real forms.
Study of quantum decorated character stacks and their quantizations.
problem Quantization of decorated character stacks and their compatibility with cutting and gluing.
method Using stratified factorization homology, extend Fock and Goncharov's construction to include stacky points.
result Construction of categorical charts and flips on quantum decorated character stacks.
We study some basic properties of the variety of characters in PSL(2,C) of a finitely generated group. In particular we give an interpretation of its points as characters of representations. We construct 3-manifolds whose variety of characters has arbitrarily many components that do not lift to SL(2,C). We also study t…
Let K be a knot in an integral homology 3-sphere and let B denote the 2-fold branched cover of the integral homology sphere branched along K. We construct a map from the slice of characters with trace free along meridians in the SL(2, C)-character variety of the knot exterior to the SL(2, C)-character variety of 2-fold…
Study character varieties of hyperbolic 3-manifolds using bundle methods.
problem Character varieties of hyperbolic 3-manifolds in once-punctured torus bundles.
method Restrict characters to the fibre and analyze branched covering maps.
result Infinite family of hyperbolic once-punctured bundles with unbounded genus.
Study the relationship between knot complements and their branched covers using abelian cord rings and SL(2,C) characters.
problem Understanding the relationship between knot complements and their branched covers.
method Utilizing Ng's abelian cord ring and SL(2,C) characters of the two-fold branched cover, focusing on augmentations and their ranks.
result Established a correspondence between trace-free SL(2,C) characters of a knot complement and augmentations, providing effective tools for finding representations.
Finite automorphisms of SL(2,C) character varieties identified.
problem Character varieties of surfaces with negative Euler characteristic.
method Algebraic automorphisms and mapping class groups studied.
result Finite extension of mapping class group identified.
Researchers describe character varieties for Hopf links, proving geometric properties.
problem Character variety geometry of Hopf links with twists.
method Geometric descriptions of irreducible and totally reducible representations.
result Complete geometric description of -character variety for .
New geometry connects super loops to Chern character.
problem Understanding super parallel transport on quotient stacks.
method Super holonomy on loop stacks to construct Chern character.
result Global equivariant Chern character from super holonomy.
Study of SU(2,1) character varieties on one-holed torus.
problem Characterize representations of mapping class group on SU(2,1) character variety.
method Explicit description of SU(2,1) character variety, use of Farey graph adaptation, and mapping class group action analysis.
result Description of an open domain of discontinuity for mapping class group action.
RNN model predicts handwritten characters from accelerometer and gyroscope data.
problem Online handwritten character recognition using sensor data.
method RNN-based neural network trained on gyroscope and accelerometer data.
result High accuracy on test data, achieving character prediction.
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…
Character-level model performs well on various languages.
problem Language modeling with minimal parameters.
method CNN and highway network over characters, followed by LSTM RNN-LM.
result Character-level model outperforms word-level/morpheme-level models with fewer parameters.
Character variety of Whitehead link described in detail.
problem Character variety of Whitehead link.
method Nice description of a Zariski open subset.
result Zariski open subset of the character variety described.
Efficient method computes -character varieties for two-generator groups.
problem Computing -character varieties for two-generator groups.
method Efficient method for two-generator groups.
result Efficient computation of -character varieties.
Proves Torelli group action is ergodic on Lie group character varieties.
problem Ergodicity of Torelli group action on compact character varieties.
method Proof based on properties of connected, semi-simple Lie groups.
result Torelli group action on compact character varieties is ergodic.
Paper proposes SA-VAE for generating stylized Chinese characters.
problem Automatic generation of stylized Chinese characters is challenging.
method Proposes Style-Aware Variational Auto-Encoder (SA-VAE) to capture content and style components.
result Shows powerful one-shot/low-shot generalization ability.
A minimal RNN model learns to generate new characters from a single example.
problem Learning efficiency and compositional ability in AI.
method Minimal RNN model with one-shot inference mechanism.
result The model can recombine previously learned substructures to generate new characters.
Reconstructs Shelstad's character identity using index theory.
problem Classifying group representations via the Langlands program.
method Geometric proof using index theory of elliptic operators in -theory.
result Evidence that index theory can be used in representation classification.
Study -character varieties of knots over fields of odd characteristic.
problem Character varieties of knots over fields of odd characteristic exhibit ramification phenomena.
method Investigate sufficient conditions for ramification using double branched covers and Alexander polynomials.
result Character varieties of knots over fields of odd characteristic can present ramification phenomena.
Study character varieties of three-holed projective plane, describing discontinuity domain.
problem Character varieties of three-holed projective plane and their properties.
method Analysis of SL(2,C) character varieties and mapping class group action.
result Description of a domain of discontinuity strictly containing primitive stable representations.
Study character varieties of odd classical pretzel knots.
problem Determine -character varieties for odd classical pretzel knots.
method Compute A-polynomial for each knot.
result Character varieties of odd classical pretzel knots computed.
Detecting essential surfaces in 3-manifolds and orbifolds using character varieties.
problem Detecting essential surfaces in 3-manifolds and orbifolds.
method Extending Culler and Shalen's construction to 3-orbifolds using character variety.
result Any slope detected on a canonical component of the character variety of a one-cusped hyperbolic 3-manifold with symmetries must be the slope of a symmetric surface.
Quantum trace maps abelian character varieties to SL2 character varieties.
problem Classifying irreducible representations of Chekhov-Fock algebras.
method Non-commutative deformation of algebraic morphisms.
result Induces birational morphism between torus and SL2 character variety.
Defines Reidemeister torsion form on 3-manifold character varieties.
problem Character variety singularities and vanishing torsion.
method Differential form on character variety, Alexander polynomial, Culler-Shalen theory.
result Torsion vanishes only at singular points, related to reducibility and Euler characteristic.
We introduce certain relative differential characters which we call Cheeger-Chern-Simons characters. These combine the well-known Cheeger-Simons characters with Chern-Simons forms. In the same way as the Cheeger-Simons characters generalize Chern-Simons invariants of oriented closed manifolds, the Cheeger-Chern-Simons …
Study character varieties in SL_2 and Kauffman skein algebras for surfaces and 3-manifolds.
problem Understanding the algebraic geometry of character varieties.
method Focus on surface and 3-manifolds groups, construct Reidemeister torsion as a rational volume form.
result Construct the Reidemeister torsion as a rational volume form on the character variety.
The paper uses attention networks for character-based handwritten text transcription.
problem Handwritten text recognition with improved character-level alignment.
method Attentional encoder-decoder networks trained on character sequences, comparing different activation functions.
result Softmax attention provides more precise character alignment than sigmoid attention.
Torus knots and provide counterexamples to a conjecture about knot contact homology.
problem Ng's conjecture about isomorphism between knot contact homology and character variety fails for certain torus knots.
method Demonstrated through the construction of ghost characters for specific torus knots.
result Counterexamples to Ng's conjecture for and torus knots.
Study character varieties of symmetric hyperbolic knots, observing different behaviors based on symmetry type.
problem Character varieties of symmetric hyperbolic knots and their reductions mod p.
method Analysis of character varieties and their reductions mod p, focusing on the presence of free or periodic symmetries.
result Character varieties exhibit different behaviors depending on whether the knots have a free or periodic symmetry.
Study of pseudo-Anosov actions on -character variety for genus 2 surfaces.
problem Characterizing pseudo-Anosov actions on -character variety.
method Analysis of mapping class group subgroups and their pseudo-Anosov elements.
result Existence of a subgroup containing infinitely many pseudo-Anosov elements with invariant rational functions.