arXiv research

New invariant for singular links via bt-algebra.

Paper explores algebraic, topological, and combinatorial properties of singular virtual braids.

Smooth algebra analysis for one-dimensional singular foliations.

New mixed singularities help classify real algebraic links.

Classifies singularities of ruled and developable surfaces using geometric algebra.

Defines a new algebra for singular foliations, extending Schwartz kernels.

Study on algebraic structures of virtual singular braid monoid and its splittable extension.

Generates moves for oriented singular links using algebraic structures.

Research examines curves of degree 8 with specific singularities.

This research extends Lie algebra actions to singular foliations.

Geometrically constructs BGG resolutions in Lie algebra type A.

In this paper we introduce a Jones-type invariant for singular knots, using a Markov trace on the Yokonuma--Hecke algebras ${\rm Y}_{d,n}(u)$ and the theory of singular braids. The Yokonuma--Hecke algebras have a natural topological interpretation in the context of framed knots. Yet, we show that there is a homomorphis…

The paper extends a geometric model using singular curves.

Study properties of algebraic threefolds with specific singularities.

Geometric models for Lie algebras from simple singularities.

We study the local symplectic algebra of curves. We use the method of algebraic restrictions to classify symplectic $T_7$ singularities. We define discrete symplectic invariants - the Lagrangian tangency orders. We use these invariants to distinguish symplectic singularities of classical $A-D-E$ singularities of planar…

Blanchet introduced certain singular cobordisms to fix the functoriality of Khovanov homology. In this paper we introduce graded algebras consisting of such singular cobordisms à la Blanchet. As the main result we give algebraic versions of these algebras using the combinatorics of arc diagrams.

Researchers classify homomorphisms for a specific algebra using singular vectors and symmetric polynomials.

Study links curve singularities to quiver mutations.

The aim of this paper is to define certain algebraic structures coming from generalized Reidemeister moves of singular knot theory. We give examples, show that the set of colorings by these algebraic structures is an invariant of singular links. As an application we distinguish several singular knots and links.

This paper calculates interaction strength for translation surfaces with multiple singularities.

This paper is a presentation, where we compute the HOMFLYPT Skein module of singular links in the 3-sphere. This calculation is based on some results previously proved by Rabenda and the author on Markov traces on singular Hecke algebras, as well as on classical techniques that allow to pass from the framework of Marko…

Study of singular knots connects knot theory with quantum algebra.

Study on virtual singular braid groups with algebraic properties and homomorphisms.

We study the local symplectic algebra of the 0-dimensional isolated complete intersection singularities. We use the method of algebraic restrictions to classify these symplectic singularities. We show that there are non-trivial symplectic invariants in this classification.

We combinatorially describe the $2$-category of singular cobordisms, called (rank one) foams, which governs the functorial version of Khovanov homology. As an application we topologically realize the type $\mathrm{D}$ arc algebra using this singular cobordism construction.

Constructs Lagrangian skeleta for curve singularities.

Study singular fibers in genus 2 algebraic fibrations and their monodromy factorizations.

Paper proves conditions for rational homology complex projective planes with singularities.

Psybrackets define invariants for complex knots and links.

The paper constructs real algebraic functions with specific singularities and preimages.

Classifies semi-algebraic surfaces up to bi-Lipschitz homeomorphisms.

We study the local symplectic algebra of curves. We use the method of algebraic restrictions to classify symplectic $W_8$ and $W_9$ singularities. We use discrete symplectic invariants to distinguish symplectic singularities of the curves. We also give the geometric description of symplectic classes.

Let X be the moduli space of SL(n,C), SU(n), GL(n,C), or U(n)-valued representations of a rank r free group. We classify the algebraic singular stratification of X. This comes down to showing that the singular locus corresponds exactly to reducible representations if there exist singularities at all. Then by relating a…

Graphs help study singular points of algebraic surfaces.

Recently the space-time foam differential algebras of generalized functions with dense singularities were introduced, motivated by the so called space-time foam structures in General Relativity with dense singularities, and by Quantum Gravity. A variety of applications of these algebras has been presented, among them, …

Conic singular sub-manifolds are Lipschitz Normally Embedded in compact non-Euclidean manifolds.

We define the singular Hecke algebra ${\mathcal H} (SB_n)$ as the quotient of the singular braid monoid algebra ${\mathbb C} (q) [SB_n]$ by the Hecke relations $σ_k^2 = (q-1) σ_k +q$, $1 \le k\le n-1$, and define the Markov traces on the sequence $\{{\mathcal H}(SB_n)\}_{n=1}^{+\infty}$ in the same way as for the Marko…

Characterizes closures of test configurations and algebraic singularity types.

Study reveals GAGA phenomenon in Poisson cohomology for plane structures with isolated singularities.

Study tangent cones of reflexive sheaves, proving existence and uniqueness.

We show that the location of the first singularity of the Upsilon function of an algebraic knot is determined by the first term of its Puiseux characteristic sequence. In many cases this gives better bounds than the tau invariant on the genus of a cobordism between algebraic knots.

Study calculates Poisson cohomology of broken Lefschetz fibrations.

Survey of algebraic structures for singular knots.

The abstract discusses how Kähler-Einstein metrics relate to algebraic geometry.

Using representations of Clifford algebras we construct indecomposable singular Riemannian foliations on round spheres, most of which are non-homogeneous. This generalizes the construction of non-homogeneous isoparametric hypersurfaces due to by Ferus, Karcher and Munzner.

New axioms for singquandles simplify applications and reveal algebraic aspects.

Study algebraic curves in C^2 using Floer theory.