arXiv research

We prove that the next possible dimension after the maximal $n^2+2n$ for the Lie algebra of local projective symmetries of a metric on a manifold of dimension $n>1$ is $n^2-3n+5$ if the signature is Riemannian or $n=2$, $n^2-3n+6$ if the signature is Lorentzian and $n>2$, and $n^2-3n+8$ elsewise. We also prove that the…

We investigate the target space geometry of supersymmetric sigma models in two dimensions with Euclidean signature, and the conditions for N=2 supersymmetry. For a real action, the geometry for the N=2 model is not the generalized Kahler geometry that arises for Lorentzian signature, but is an interesting modification …

Researchers extend geodesic orbit properties to pseudo-Riemannian nilmanifolds of specific signature.

A flat pseudo-Euclidean Lie algebra is a real Lie algebra with a non degenerate symmetric bilinear form and a left symmetric product whose the commutator is the Lie bracket and such that the left multiplications are skew-symmetric. We show that the center of a flat pseudo-Euclidean nilpotent Lie algebra of signature $(…

(This is a revised version of the paper) - In the present paper we study the geometry of doubly extended Lie groups with their natural biinvariant metric. We describe the curvature, the holonomy and the space of parallel spinors. This is completely done for all simply connected groups with biinvariantmetric of Lorentzi…

The classifications of holonomy groups in Lorentzian and in Euclidean signature are quite different. A group of interest in Lorentzian signature in n dimensions is the maximal proper subgroup of the Lorentz group, SIM(n-2). Ricci-flat metrics with SIM(2) holonomy were constructed by Kerr and Goldberg, and a single four…

We present an approach to solvable pseudo-Riemannian symmetric spaces based on papers of M.Cahen, M.Parker and N.Wallach. Thereby we reproduce the classification of solvable symmetric triples of Lorentzian signature $(1,n-1)$ and complete the case of signature $(2,n-2)$. Moreover we discuss the topology of non-simply-c…

We derive the topological obstruction to spin-Klein cobordism. This result has implications for signature change in general relativity, and for the $N=2$ superstring.

The paper explores existence of specific almost complex manifolds with unique Betti numbers.

We develop the classification of weakly symmetric pseudo--riemannian manifolds $G/H$ where $G$ is a semisimple Lie group and $H$ is a reductive subgroup. We derive the classification from the cases where $G$ is compact, and then we discuss the (isotropy) representation of $H$ on the tangent space of $G/H$ and the signa…

We study the problem of recovering a function on a pseudo-Riemannian manifold from its integrals over all null geodesics in three geometries: pseudo-Riemannian products of Riemannian manifolds, Minkowski spaces and tori. We give proofs of uniqueness anc characterize non-uniqueness in different settings. Reconstruction …

The study finds limits on dimensions of certain scales and fields for conformal manifolds.

Werner Meyer constructed a cocycle in $H^2(Sp(2g, \mathbb{Z}); \mathbb{Z})$ which computes the signature of a closed oriented surface bundle over a surface, with fibre a surface of genus g. By studying properties of this cocycle, he also showed that the signature of such a surface bundle is a multiple of 4. In this pap…

We study the geometric structure of Lorentzian spin manifolds, which admit imaginary Killing spinors. The discussion is based on the cone construction and a normal form classification of skew-adjoint operators in signature $(2,n-2)$. Derived geometries include Brinkmann spaces, Lorentzian Einstein-Sasaki spaces and cer…

In a given 4d spacetime bakcground, one can often construct not one but a family of distinct N=2 string theories. This is due to the multiple ways N=2 superconformal algebra can be embedded in a given worldsheet theory. We formulate the principle of obtaining different physical theories by gauging different embeddings …

We prove the following statement: Let g be a light-line-complete pseudo-Riemannian Einstein metric of indefinite signature on a connected (n>2)-dimensional manifold M. Assume that a conformally equivalent metric is also Einstein. Then, the metrics are proportional with a constant coefficient. If in addition the manifol…

There are three types of hypersurfaces in a pseudoconformal space C^n_1 of Lorentzian signature: spacelike, timelike, and lightlike. These three types of hypersurfaces are considered in parallel. Spacelike hypersurfaces are endowed with a proper conformal structure, and timelike hypersurfaces are endowed with a conform…

The target space geometry of abelian vector multiplets in ${\cal N}= 2$ theories in four and five space-time dimensions is called special geometry. It can be elegantly formulated in terms of Hessian geometry. In this review, we introduce Hessian geometry, focussing on aspects that are relevant for the special geometrie…

In an earlier paper we developed the classification of weakly symmetric pseudo--riemannian manifolds $G/H$ where $G$ is a semisimple Lie group and $H$ is a reductive subgroup. We derived the classification from the cases where $G$ is compact. As a consequence we obtained the classification of semisimple weakly symmetri…

We study the existence of cocompact lattices in Lie groups with bi-invariant metric of signature $(2,n-2)$. We assume in addition that the Lie groups under consideration are simply-connected, indecomposable and solvable. Then their centre is one- or two-dimensional. In both cases, a parametrisation of the set of such L…

Using Gauge theoretical techniques employed by Lisca for 2-bridge knots and by Greene-Jabuka for 3-stranded pretzel knots, we show that no member of the family of Montesinos knots M(0;[m_1+1,n_1+2],[m_2+1,n_2+2],q), with certain restrictions on m_i, n_i, and q, can be (smoothly) slice. Our techniques use Donaldson's di…

A parameter-free statistical model is used to study multiplicity signatures for coherent production of charged-pairs of parabosons of order p=2 in comparison with those arising in the case of ordinary bosons, p=1. Two non-negative real parameters arise because "ab" and "ba" are fundamentally distinct pair operators of …

An indecomposable Lie group with Riemannian bi-invariant metric is always simple and hence Einstein. For indefinite metrics this is no longer true, not even for simple Lie groups. We study the question of whether a semi-Riemannian bi-invariant metric is conformal to an Einstein metric. We obtain results for all three c…

We discuss the conditions for additional supersymmetry and twisted supersymmetry in N = (2, 2) supersymmetric non-linear sigma models described by one left and one right semi-chiral superfield and carrying a pair of non-commuting complex structures. Focus is on linear non-manifest transformations of these fields that h…

Topological gauge theories in four dimensions which admit surface operators provide a natural framework for realizing homological knot invariants. Every such theory leads to an action of the braid group on branes on the corresponding moduli space. This action plays a key role in the construction of homological knot inv…

Defines and extends flat pseudo-Riemannian F-Lie algebras.

The paper revisits expected signatures in semimartingale models, providing new formulae and simplifying complexity.

Defines knot signature invariant using G-signature theorem.

Deep signature/log-signature FBSDE algorithm improves accuracy and training time.

A well-known property of the signature of closed oriented 4n-dimensional manifolds is Novikov additivity, which states that if a manifold is split into two manifolds with boundary along an oriented smooth hypersurface, then the signature of the original manifold equals the sum of the signatures of the resulting manifol…

Maximum Levine-Tristram signature of torus knots follows a reduction formula.

New findings on mesh group-planes validate Signature-inverse Theorem under specific conditions.

We study various topological invariants on a torsional geometry in the presence of a totally anti-symmetric torsion H under the closed condition dH = 0, which appears in string theory compactification scenarios. By using the identification between the Clifford algebra on the geometry and the canonical quantization cond…

Introduces flat discrete signatures for financial data analysis.

This is a sequel to the paper "The signature package on Witt spaces, I. Index classes" by the same authors. In the first part we investigated, via a parametrix construction, the regularity properties of the signature operator on a stratified Witt pseudomanifold, proving, in particular, that one can define a K-homology …

We define the Analytical signature, the Hodge signature and the de Rham signature for a foliated manifold with boundary with foliation transverse to the boundary. We show that all these signatures coincide and a Hirzebruch formula is valid.

New methods price American options in rough volatility models.

The paper examines the consistency of Lasso regression applied to signature analysis of time series data.

Study signatures of torus links and their cores using Neumann's equivariant signatures and Hirzebruch's formula.

This paper extends the C*-signature to non-Witt spaces using noncommutative geometric methods.

Paper generalizes path signature using fractional calculus for improved machine learning.

We present a novel method for extracting cancer signatures by applying statistical risk models (http://ssrn.com/abstract=2732453) from quantitative finance to cancer genome data. Using 1389 whole genome sequenced samples from 14 cancers, we identify an "overall" mode of somatic mutational noise. We give a prescription …

pySigLib speeds up signature-based computations on CPUs and GPUs.

Efficiently computes sparse signature coefficients using kernels.

New method calculates signatures of biquotients.

Paper introduces branched signature model for efficient computation and data-driven applications.

Link signature limit depends on linking matrix under specific polynomial condition.

Path signatures improve hedging of exotic derivatives in non-Markovian models.