arXiv research

New algebraic structures called cyclic Lie-Rinehart algebras are defined.

Unified framework LPCD optimizes quantization of complex submodules.

Study perturbations of submodules in Drury-Arveson space, finding smooth vector bundles with Hermitian connections.

The paper introduces lattice homology for integrally closed submodules and applies it to geometric invariants.

Solves Lempert's question on Nakano semi-positivity preservation.

Study ribbon homology concordances using link Floer homology.

We look at Poisson geometry taking the viewpoint of singular foliations, understood as suitable submodules generated by Hamiltonian vector fields rather than partitions into (symplectic) leaves. The class of Poisson structures which behave best from this point of view, are those whose submodule generated by Hamiltonian…

A geodesic orbit manifold (GO manifold) is a Riemannian manifold (M,g) with the property that any geodesic in M is an orbit of a one-parameter subgroup of a group G of isometries of (M,g). The metric g is then called a G-GO metric in M. For an arbitrary compact homogeneous manifold M=G/H, we simplify the general proble…

In this paper we prove some properties of the nonabelian cohomology $H^1(A,G)$ of a group $A$ with coefficients in a connected Lie group $G$. When $A$ is finite, we show that for every $A$-submodule $K$ of $G$ which is a maximal compact subgroup of $G$, the canonical map $H^1(A,K)\to H^1(A,G)$ is bijective. In this cas…

A class of Z_2-graded Lie algebra and Lie superalgebra extensions of the pseudo-orthogonal algebra of a spacetime of arbitrary dimension and signature is investigated. They have the form g = g_0 + g_1, with g_0 = so(V) + W_0 and g_1 = W_1, where the algebra of generalized translations W = W_0 + W_1 is the maximal solva…

New torsion patterns found in Khovanov homology of link diagrams.

We consider the Lie algebra of all vector fields on a contact manifold as a module over the Lie subalgebra of contact vector fields. This module is split into a direct sum of two submodules: the contact algebra itself and the space of tangent vector fields. We study the geometric nature of these two modules.

The paper is devoted to the study of geodesic orbit Riemannian spaces that could be characterize by the property that any geodesic is an orbit of a 1-parameter group of isometries. The main result is the classification of compact simply connected geodesic orbit Riemannian spaces $G/H$ with two irreducible submodules in…

This paper shows hyperbolic knots can have arbitrarily large torsion in knot Floer homology.

We study geodesics in generalized Wallach spaces which are expressed as orbits of products of three exponential terms. These are homogeneous spaces $M=G/K$ whose isotropy representation decomposes into a direct sum of three submodules $\frak{m}=\frak{m}_1\oplus\frak{m}_2\oplus\frak{m}_3$, satisfying the relations $[\fr…

Researchers compute the Kauffman bracket skein module of a specific 3-manifold.

New method for linear connections in ODEs with constraints.

Let ${\mathcal F}_λ(\mathbb{S}^n)$ be the space of tensor densities on $\mathbb{S}^n$ of degree $λ$. We consider this space as an induced module of the nonunitary spherical series of the group $\mathrm{SO}_0(n+1,1)$ and classify $(\mathrm{so}(n+1,1),\mathrm{SO}(n+1))$-sim$unitary submodules of${\mathcal F}_λ(\mathbb{S…

Is cognition a collection of loosely connected functions tuned to different tasks, or can there be a general learning algorithm? If such an hypothetical general algorithm did exist, tuned to our world, could it adapt seamlessly to a world with different laws of nature? We consider the theory that predictive coding is s…

This paper introduces 'General Cyclical Training' for neural networks.

The paper generalizes cyclic metrics in homogeneous Finsler geometry.

In this paper we study the connections between cyclic presentations of groups and branched cyclic coverings of (1,1)-knots. In particular, we prove that every n-fold strongly-cyclic branched covering of a (1,1)-knot admits a cyclic presentation for the fundamental group encoded by a Heegaard diagram of genus n.

Characterizes non-degenerate cyclic metric Lie algebras.

Proves almost profinite rigidity for certain free-by-cyclic groups.

We study the connections among the mapping class group of the twice punctured torus, the cyclic branched coverings of (1,1)-knots and the cyclic presentations of groups. We give the necessary and sufficient conditions for the existence and uniqueness of the n-fold strongly-cyclic branched coverings of (1,1)-knots, thro…

New cyclicity measures defined in weighted Besov spaces, with stability and geometric analysis.

We refine the cyclic cohomological apparatus for computing the Hopf cyclic cohomology of the Hopf algebras associated to infinite primitive Cartan-Lie pseudogroups, and for the transfer of their characteristic classes to foliations. The main novel feature is the precise identification as a Hopf cyclic complex of the im…

In this paper, we study quandles of cyclic type, which form a particular subclass of finite quandles. The main result of this paper describes the set of isomorphism classes of quandles of cyclic type in terms of certain cyclic permutations. By using our description, we give a direct classification of quandles of cyclic…

We show, finitely generated rational $\mathsf{VIC}_{\mathbb Q}$-modules and $\mathsf{SI}_{\mathbb Q}$-modules are uniformly representation stable and all their submodules are finitely generated. We use this to prove two conjectures of Church and Farb, which state that the quotients of the lower central series of the To…

Cyclical learning rates improve DRL performance without manual tuning.

The paper investigates cyclic arbitrage opportunities in decentralized exchanges.

Unified rigidity theorem for cyclic and alternating surfaces.

In spin geometry, traceless cyclic homogeneous Riemannian manifolds equipped with a homogeneous spin structure can be viewed as the simplest manifolds after Riemannian symmetric spin spaces. In this paper, we give some characterizations and properties of cyclic and traceless cyclic homogeneous Riemannian manifolds and …

We give a sufficient condition under which vanishing property of Cochran-Orr-Teichner knot concordance obstructions splits under connected sum. The condition is described in terms of self-annihilating submodules with respect to higher-order Blanchfield linking forms. This extends results of Levine and the authors on di…

The abstract introduces a new cyclic structure for surfaces.

We give a construction of cyclic cocycles representing the equivariant characteristic classes of equivariant bundles. Our formulas generalize Connes' Godbillon-Vey cyclic cocycle. An essential tool of our construction is Connes-Moscovici's theory of cyclic cohomology of Hopf algebras.

Study integrable discretizations of cyclic systems with circular coordinate lines.

A surgery on a knot in 3-sphere is called SU(2)-cyclic if it gives a manifold whose fundamental group has no non-cyclic SU(2) representations. Using holonomy perturbations on the Chern-Simons functional, we prove that the distance of two SU(2)-cyclic surgery coefficients is bounded by the sum of the absolute values of …

New definite 4-manifolds found with non-cyclic groups.

We classify $SU(2)$-cyclic and $SU(2)$-abelian 3-manifolds, for which every representation of the fundamental group into $SU(2)$ has cyclic or abelian image respectively, among geometric 3-manifolds which are not hyperbolic. As an application, we give examples of hyperbolic 3-manifolds which do not admit degree-1 maps …

Cyclic projections in Hadamard spaces can be irregular, unlike in Hilbert spaces.

Cyclic covers of knots uniquely determine the original knot.

Geodesic orbit metrics on real flag manifolds identified.

The motivation of this work is to define cohomology classes in the space of knots that are both easy to find and to evaluate, by reducing the problem to simple linear algebra. We achieve this goal by defining a combinatorial graded cochain complex, such that the elements of an explicit submodule in the cohomology defin…

New framework for cyclic quantum causal models with graph separation property.

New Heegaard Floer homology for orbifolds with cyclic singularities.

A central result here is the computation of the entire cyclic homology of canonical smooth subalgebras of stable continuous trace C*-algebras having smooth manifolds M as their spectrum. More precisely, the entire cyclic homology is shown to be canonically isomorphic to the continuous periodic cyclic homology for these…

Let $M$ be an irreducible, compact, connected, orientable 3-manifold whose boundary is a torus. We show that if $M$ is hyperbolic, then it admits at most six finite/cyclic fillings of maximal distance 5. Further, the distance of a finite/cyclic filling to a cyclic filling is at most 2. If $M$ has a non-boundary-paralle…