arXiv research

Paper derives localization formula for $S^1$-action and equivariant η-invariants.

It is proved that the category of simplicial complete bornological spaces over $\mathbb R$ carries a combinatorial monoidal model structure satisfying the monoid axiom. For any commutative monoid in this category the category of modules is also a monoidal model category with all cofibrant objects being flat. In particu…

Motivated by deformation quantization, we introduced in an earlier work the notion of formal Morita equivalence in the category of $^*$-algebras over a ring $\ring C$ which is the quadratic extension by $\im$ of an ordered ring $\ring R$. The goal of the present paper is twofold. First, we clarify the relationship betw…

Researchers found only one hyperbolic structure for Borromean rings.

Paper computes hyperbolic structure of Borromean rings complement.

Differential K-theory gets a $λ$-ring structure.

BRTR improves robust tensor completion with automatic rank detection.

Study calculates ring structure in instanton homology for a surface with points.

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

New Frobenius manifold structures found on Dicyclic group orbits.

A new invariant of Poisson manifolds, a Poisson K-ring, is introduced. Hypothetically, this invariant is more tractable than such invariants as Poisson (co)homology. A version of this invariant is also defined for arbitrary algebroids. Basic properties of the Poisson K-ring are proved and the Poisson K-rings are calcul…

The paper studies the metric and algebraic structures on section rings of projective manifolds.

A C-infinity ring is a set equipped with n-ary operations corresponding to smooth n-ary functions on the real line (satisfying natural axioms). We prove that the cosimplicial abelian group associated to the de Rham complex of Euclidean space has the structure of a cosimplicial C-infinity ring. We also analyse the notio…

We give a new description of the ring structure on the differential characters of a smooth manifold via the smooth hyperspark complex. We show the explicit product formula, and as an application, calculate the product for differential characters of the unit circle. Applying the presentation of spark classes by smooth h…

Presented an algebra structure for a specific geometric surface.

Let G be a compact, simply connected Lie group. We develop a `quantization functor' from pre-quantized quasi-Hamiltonian G-spaces at level k to the fusion ring (Verlinde algebra) R_k(G). The quantization Q(M) is defined as a push-forward in twisted equivariant K-homology. It may be computed by a fixed point formula, si…

We review the polynomial structure of the topological string partition functions as solutions to the holomorphic anomaly equations. We also explain the connection between the ring of propagators defined from special Kähler geometry and the ring of almost-holomorphic modular forms defined on modular curves.

We determine the structure of the Hodge ring, a natural object encoding the Hodge numbers of all compact Kaehler manifolds. As a consequence of this structure, there are no unexpected relations among the Hodge numbers, and no essential differences between the Hodge numbers of smooth complex projective varieties and tho…

Researchers find Frobenius manifold structures on orbits spaces of finite groups.

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

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

We prove, under some mild conditions, that the equivariant twisted K-theory group of a crossed module admits a ring structure if the twisting 2-cocycle is 2-multiplicative. We also give an explicit construction of the transgression map $T_1: H^*(Γ;A) \to H^{*-1}((N\rtimes Γ;A)$ for any crossed module $N\to Γ$ and prove…

AI can identify simple groups and match algebraic tables, even with limited training.

New cohomology ring for complex manifolds with group action.

Explains how pre-symplectic structures can be changed.

We demonstrate how by using the intersection theory to calculate the cohomology of $G_2$-manifolds constructed by using the generalized Kummer construction. For one example we find the generators of the rational cohomology ring and describe the product structure.

We give a presentation for the Floer cohomology ring $HF^*(Σ\times S^1)$, where $Σ$ is a Riemann surface of genus bigger than one, which coincides with the conjectural presentation for the quantum cohomology ring of the moduli space of flat SO(3)-connections of odd degree over $Σ$. We study the spectrum of the action o…

In the first part of the paper we construct a ring structure on the rational cobordism classes of Morin maps (i. e. smooth generic maps of corank 1). We show that associating to a Morin map its singular strata defines a ring homomorphism to $Ω_* \otimes \Q$, the rational oriented cobordism ring. This is proved by analy…

Motivated by orbifold string theory, we introduce orbifold cohomology group for any almost complex orbifold and orbifold Dolbeault cohomology for any complex orbifold. Then, we show that our new cohomology group satisfies Poincare duality and has a natural ring structure. Some examples of orbifold cohomology ring are c…

We prove that two closed oriented 3-manifolds have isomorphic quintuplets (homology, space of spin structures, linking pairing, cohomology rings, Rochlin function) if, and only if, they belong to the same class of a certain surgery equivalence relation introduced by Goussarov and Habiro.

Defines pre-Kähler structures and their properties.

A new isomorphism connects fundamental group ring quotients to cohomology.

Probabilistic theory counts intersections in Riemannian spaces.

We define an integer graded symplectic Floer cohomology and a Fintushel-Stern type spectral sequence which are new invariants for monotone Lagrangian sub-manifolds and exact isotopes. The Z-graded symplectic Floer cohomology is an integral lifting of the usual Z_Sigma(L)-graded Floer-Oh cohomology. We prove the Kunneth…

We prove that the Farrell-Jones isomorphism conjecture for non-connective algebraic K-theory for a discrete group G and a coefficient ring R holds true if G belongs to the class of groups acting on trees, under certain conditions on G (see theorem 0.5 below) and if the coefficient ring R is either regular or hereditary…

In this article, we introduce symbol calculus on a projective scheme. Using holomorphic Poisson structures, we construct deformations of ring structures for structure sheaves on projective spaces.

We extend the well-known Borromean and Brunnian rings to new higher order versions. Then we suggest an extension of the connection between Efimov states in cold gases and Borromean and Brunnian rings to these new higher order links. This gives rise to a whole new hierarchy of possible states with Efimov states at the b…

A new tensor ring mixture model improves density estimation efficiency.

Abstract: Tangent categories get a Cartan calculus with scalar multiplication by a commutative ring.

We construct a new family of toric manifolds generating the unitary bordism ring. Each manifold in the family is the complex projectivisation of the sum of a line bundle and a trivial bundle over a complex projective space. We also construct a family of special unitary quasitoric manifolds which contains polynomial gen…

New algorithm reduces communication bandwidth for large-scale deep learning training.

The abstract discusses conditions for stable almost complex structures on specific 10-manifolds.

An almost-direct product of free groups is an iterated semidirect product of finitely generated free groups in which the action of the constituent free groups on the homology of one another is trivial. We determine the structure of the cohomology ring of such a group. This is used to analyze the topological complexity …

We define a Riemannian structure as a pre-homogeneous geometric structure with curvature R. We show that R=0 if and only if the underlying metric has constant curvature. We define pre-homogeneous geometric structures and pose some problems.

The paper introduces statistical and geometric structures on anti-commutable pre-Leibniz algebroids.

Integrates C-bracket and Vaisman algebroid structures in double field theory.

The paper proposes a method to compute higher infinitesimals in numerical and symbolic analysis.

Let $M$ be a closed, oriented manifold of dimension $d$. Let $LM$ be the space of smooth loops in $M$. Chas and Sullivan recently defined a product on the homology $H_*(LM)$ of degree $-d$. They then investigated other structure that this product induces, including a Batalin -Vilkovisky structure, and a Lie algebra str…