arXiv research

Study of knot group completions links Alexander polynomials.

Researchers found only one hyperbolic structure for Borromean rings.

We develop a class of integrals on a manifold M called exponential iterated integrals, an extension of K. T. Chen's iterated integrals. It is shown that the matrix entries of any upper triangular representation of the fundamental group of M can be expressed via these new integrals. The ring of exponential iterated inte…

A new isomorphism connects fundamental group ring quotients to cohomology.

Classifies cobounded hyperbolic actions of metabelian groups.

We represent the coordinate ring of algebraic hulls (which are generalizations of the Malcev completions of nilpotent groups for solvable groups) of solvmanifolds $G/Γ$ by using Miller's exponential iterated integrals (which are extensions of Chen's iterated integrals) of invariant differential forms.

Researchers compute torsion for homology cylinders, proving it a finite-type invariant.

Bayesian model improves image completion accuracy by automatically learning low rank structure.

In this paper we continue the study of generic properties of the Novikov complex, began in the work "The incidence coefficients in the Novikov complex are generically rational functions" ( dg-ga/9603006). For a Morse map $f:M\to S^1$ there is a refined version of Novikov complex, defined over the Novikov completion of …

Computes group of ring motions for a specific link structure.

Paper proves tensor ring completion with high probability using convex optimization.

Division algorithm for surface group rings yields standard complexes and cohomological dimensions.

A hyperbolic 3-simplex reflection group is a Coxeter group arising as a lattice in the isometry group of hyperbolic 3-space, with fundamental domain a geodesic simplex (possibly with some ideal vertices). The classification of these groups is known, and there are exactly 9 cocompact examples, and 23 non-cocompact examp…

Global group laws connect equivariant bordism rings to formal group laws.

Study Coxeter groups over fusion rings and their geometric realisations.

The paper proves conditions for self-covering manifolds to be fiber bundles over a circle.

It is proved that the ring of invariants of the standard smooth completion of a Kac-Moody Lie algebra is functionally generated by two elements: the coefficient of the center and the Killing form.

Non-Euclidean number rings have non-integral Steinberg modules.

Study algebraic K-theory for specific groups of non-orientable surfaces.

New Frobenius manifold structures found on Dicyclic group orbits.

Study shows $L^{2}$-Betti numbers vanish for certain matrix groups over rings, proving non-acylindrical hyperbolicity.

We construct an enhanced version of knot contact homology, and show that we can deduce from it the group ring of the knot group together with the peripheral subgroup. In particular, it completely determines a knot up to smooth isotopy. The enhancement consists of the (fully noncommutative) Legendrian contact homology a…

We study isomorphism classes of symplectic dual pairs P <- S -> P-, where P is an integrable Poisson manifold, S is symplectic, and the two maps are complete, surjective Poisson submersions with connected and simply-connected fibres. For fixed P, these Morita self-equivalences of P form a group Pic(P) under a natural `…

Study properties of group rings of three-manifold groups.

Researchers explore representations of 3-manifold groups over finite commutative rings.

New method computes automorphisms of surface groups using skein algebras.

New hyperbolic manifolds found with same trace ring.

Paper computes hyperbolic structure of Borromean rings complement.

The paper explores zero-divisors and idempotents in quandle rings, proving their absence in certain cases.

Generalizes Quillen's theorem to equivariant settings.

Investigates neural codes and their embeddings, proving conjectures and introducing new code types.

The paper proves stabilization in hypersurface sections using Grothendieck rings and probabilistic methods.

Robust tensor ring completion improves tensor recovery accuracy and efficiency.

We give an explicit formula for the cohomology of a right angled Artin group with group ring coefficients in terms of the cohomology of its defining flag complex.

Explains the Borromean rings, icosahedron, and Poincaré homology sphere.

Compute group cohomology for mapping class group with non-symplectic coefficients.

Researchers compute the cohomology ring of a foliation defined by a group action.

Study calculates the modulus of Korányi ellipsoidal rings in Heisenberg groups.

The paper defines a ring structure in twisted equivariant $KK$-theory for Lie groups.

Researchers created group presentations for specific Bianchi groups.

Study SL(2,C) character schemes for finitely generated groups.

Calculates cobordism ring of stably almost complex C_p-manifolds.

BRTR improves robust tensor completion with automatic rank detection.

In a previous paper, the authors defined an equivariant version of the so-called Saito duality between the monodromy zeta functions as a sort of Fourier transform between the Burnside rings of an abelian group and of its group of characters. Here a so-called enhanced Burnside ring $\widehat{B}(G)$ of a finite group $G$…

Computes cohomology groups for NEC groups, focusing on Fuchsian groups.

We study the universal character ring of some families of one-relator groups. As an application, we calculate the universal character ring of two-generator one-relator groups whose relators are palindrome, and, in particular, of the (-2,2m+1,2n+1)-pretzel knot for all integers m and n. For the (-2,3,2n+1)-pretzel knot,…

The purpose of this paper is to connect two subjects: the theory of quantum integrable systems (complete commutative rings of differential operators), and differential Galois theory. We define quantum completely integrable systems (QCIS), algebraically integrable QCIS, the differential Galois group of a QCIS. We show t…

Let $G$ be a compact connected Lie group acting on a stable complex manifold $M$ with equivariant vector bundle $E$. Besides, suppose $φ$ is an equivariant map from $M$ to the Lie algebra $\mathfrak{g}$. We can define some equivalence relation on the triples $(M, E, φ)$ such that the set of equivalence classes form an …