A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Most Finsler metrics have infinite-dimensional holonomy groups.
Proves uniqueness of embedding complex manifold into infinite-dimensional space.
Study shows how Poisson brackets factor on infinite dimensional manifolds.
We define submersions f between manifolds M and N modelled on locally convex spaces. If the range N is finite-dimensional or a Banach manifold, then these coincide with the naive notion of a submersion. We study pre-images of submanifolds under submersions and pre-images under mappings whose differentials have dense im…
The study defines divergence for multivector fields on infinite-dimensional manifolds.
This paper explores topological aspects of index theory for infinite-dimensional manifolds.
Introduces infinite-dimensional differential geometry using Bastiani calculus.
The abstract discusses transversality for infinite dimensional manifolds.
We construct a infinite-dimensional manifold structure adapted to analytic Lie pseudogroups of infinite type. More precisely, we prove that any isotropy subgroup of an analytic Lie pseudogroup of infinite type is a regular infinite-dimensional Lie group, modelled on a locally convex strict inductive limit of Banach spa…
The theory of product preserving functors and Weil functors is partly extended to infinite dimensional manifolds, using the theory of -algebras.
A manifold's co-invariant cohomology can be infinite-dimensional.
Following the approach of Carlet et al.(2011)\cite{CDM}, we construct a class of infinite-dimensional Frobenius manifolds underlying the Toda lattice hierarchy, which are defined on the space of pairs of meromorphic functions with possibly higher-order poles at the origin and at infinity. We also show a connection betw…
We construct a class of infinite-dimensional Frobenius manifolds on the space of pairs of certain even functions meromorphic inside or outside the unit circle. Via a bi-Hamiltonian recursion relation, the principal hierarchies associated to such Frobenius manifolds are found to be certain extensions of the dispersionle…
Spray-invariant sets maintain geodesics on infinite-dimensional manifolds.
Book on infinite-dimensional Lie groups, covering basics and various classes.
In this paper we propose a new treatment about infinite dimensional manifolds, using the language of category and functor. Our definition of infinite dimensional manifolds is a natural generalization of finite dimensional manifolds in the sense that de Rham cohomology and singular cohomology can be naturally defined an…
Using symplectic techniques and spectral analysis of smooth paths of self-adjoint operators, we characterize the set of conjugate instants along a geodesic in an infinite dimensional Riemannian Hilbert manifold.
Generalized Stacey-Roberts lemma for Banach manifolds.
Existence of balanced embedding proved for complex manifold into infinite-dimensional space.
In this paper we study the homogeneous Kaehler manifolds (h.K.m.) which can be Kaehler immersed into finite or infinite dimensional complex space forms. On one hand we completely classify the h.K.m. which can be Kaehler immersed into a finite or infinite dimensional complex Euclidean or hyperbolic space. Moreover, we e…
We introduce a structure of an infinite-dimensional Frobenius manifold on a subspace in the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/infinity respectively. The dispersionless 2D Toda equations are embedded into a bigger integrable hierarchy associated with this Frobeniu…
The paper extends Cartan development to infinite dimensional Lie groups.
Universal approximation theorem for differentiable maps on infinite-dimensional manifolds
We present the construction of an infinite dimensional Banach manifold of quantum mechanical states on a Hilbert space H using different types of small perturbations of a given Hamiltonian. We provide the manifold with a flat connection, called the exponential connection, and comment on the possibility of introducing t…
Generalizes neural network approximation to infinite-dimensional manifolds and derivatives.
We prove a Frobenius theorem for Banach distributions on manifolds that are modelled over locally convex spaces. Moreover, we recall how Frobenius theorems can be applied to infinite-dimensional Lie groups and obtain, that given a Lie subalgebra of the Lie algebra of a Lie group that is modelled over a locally convex s…
The abstract extends deformation and tangent groupoid constructions to infinite-dimensional manifolds.
Noncompact Ricci-flat solutions have infinite unstable dimensions.
Constructs infinite-dimensional Siegel disc as symplectic and Kaehler quotient.
We present several principal bundles of embeddings of compact manifolds (with or without boundary) whose base manifolds are nonlinear Grassmannians. We study their infinite dimensional differential manifold structure in the Fréchet category. This study is motivated by the occurrence of such objects in the geometric Lag…
Chern-Weil and Chern-Simons theory extend to certain infinite-rank bundles that appear in mathematical physics. We discuss what is known of the invariant theory of the corresponding infinite-dimensional Lie groups. We use these techniques to detect cohomology classes for spaces of maps between manifolds and for diffeom…
Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally con…
Optimizes shapes on non-standard manifolds.
It is proved that the moduli space of all connected compact orientable embedded minimal affine Lagrangian submanifolds of a complex equiaffine space constitutes an infinite dimensional Frechet manifold (if it is not the empty set). The moduli space of all connected compact orientable metric Lagrangian embedded surfaces…
We have been studying the index theory for some special infinite-dimensional manifolds with a "proper cocompact" actions of the loop group LT of the circle T, from the viewpoint of the noncommutative geometry. In this paper, we will introduce the LT-equivariant KK-theory and we will construct three KK-elements: the ind…
Infinite-dimensional contact geometry explored.
We discuss possible extensions of the classical Chern-Weil formalism to an infinite dimensional setup. This is based on joint work with Steven Rosenberg, joint work with Simon Scott and joint work with Jouko Mickelsson.
Let be a separable Hilbert space, possibly infinite dimensional. Let $\St(p,V)$ be the Stiefel manifold of orthonormal frames of vectors in , and let $\Gr(p,V)$ be the Grassmann manifold of dimensional subspaces of . We study the distance and the geodesics in these manifolds, by reducing the matter to…
Symplectic method solves infinite-dimensional Schrödinger equations.
Research covers geometry, analysis, and integration on infinite-dimensional spaces.
We describe a relation between the periodic one-dimensional Toda lattice and the quantum cohomology of the periodic flag manifold (an infinite-dimensional Kaehler manifold). This generalizes a result of Givental and Kim relating the open Toda lattice and the quantum cohomology of the finite-dimensional flag manifold. W…
This paper tackles the topology of infinite-dimensional fiber spaces.
Recently, we developed a method for the study of holonomy properties of non-Riemannian Finsler manifolds and obtained that the holonomy group can not be a compact Lie group, if the Finsler manifold of dimension has non-zero constant flag curvature. The purpose of this paper is to move further, exploring the holon…
Study infinite-dimensional Toda manifold at irregular singularity, revealing non-uniqueness of formal solutions.
Diffeologies unify infinite-dimensional geometry and PDEs, enhancing classical function spaces.
Study geodesics on infinite-dimensional manifolds using Finsler structures.
Develops a mathematical framework for causal fermion systems in infinite dimensions.
Develops Schouten-Nijenhuis bracket on infinite-dimensional manifolds.