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.
New findings on asymptotic property C in infinite dimensional spaces.
The paper proves an equality linking torsion, volume, and a product for hyperbolic 3-manifolds.
The theory of product preserving functors and Weil functors is partly extended to infinite dimensional manifolds, using the theory of -algebras.
The paper proves an equality involving torsion, volume, and a product for hyperbolic 3-manifolds.
We show that all non-trivial continuous endomorphisms of the circle group are topologically mixing. We also show that there exists a large infinite class of continuous endomorphisms of any n-dimensional torus group which are topologically mixing. Lastly, we prove that any continuous endomorphism on an abelian polish se…
Let X and Y be infinite graphs, such that the automorphism group of X is nonamenable, and the automorphism group of Y has an infinite orbit. We prove that there is no automorphism-invariant measure on the set of spanning trees in the direct product X times Y. This implies that the minimal spanning forest corresponding …
Maximal open subset found for product of CAT(-1) spaces.
Study stability of operators on warped product manifolds.
Study irrational rotations and construct 2-filling rays on infinite type surfaces.
Infinite volumes of Bergman spaces on product manifolds.
Based on the proof of Labastida-Mari{ñ}o-Ooguri-Vafa conjecture \cite{lmov}, we derive an infinite product formula for Chern-Simons partition functions, the generating function of quantum $\fsl_N$ invariants. Some symmetry properties of the infinite product will also be discussed.
Study hot spots on warped product manifolds and infinite cones.
We show that the Cartesian product of three hereditarily infinite dimensional compact metric spaces is never hereditarily infinite dimensional. It is quite surprising that the proof of this fact (and this is the only proof known to the author) essentially relies on algebraic topology.
Graph of groups palindromic width mostly infinite.
One of the goals of this article is to define a an unified setting adapted to the description of means (normalized integrals or invariant means) on an infinite product of measured spaces with infinite measure. We first remark that some known examples coming from the theory of metric measured spaces and also from oscill…
In various classes of infinite groups, we identify groups that are presentable by products, i.e. groups having finite index subgroups which are quotients of products of two commuting infinite subgroups. The classes we discuss here include groups of small virtual cohomological dimension and irreducible Zariski dense sub…
Based on the orthogonal Labastida-Mari{ñ}o-Ooguri-Vafa conjecture made by L. Chen & Q. Chen [5], we derive an infinite product formula for Chern-Simons partition functions, which generalizes the Liu-Peng's [19] recent results to the orthogonal case. Symmetry property of this new infinite product structure is also discu…
We show that there is a well-defined cap-product structure on the Fintushel-Stern spectral sequence. Hence we obtain the induced cap-product structure on the ${\BZ}_8$-graded instanton Floer homology. The cap-product structure provides an essentially new property of the instanton Floer homology, from a topological poin…
Study of pure mapping class groups on infinite graphs.
We present an approach to cohomological dimension theory based on infinite symmetric products and on the general theory of dimension called the extension dimension. The notion of the extension dimension $\ExD(X)$ was introduced by A.N.Dranishnikov \cite {D} in the context of compact spaces and CW complexes. This pa…
Graph products inherit Morse local-to-global property from their components.
Study finds infinite conformal classes on product manifolds.
Study the Lax equation in infinite-dimensional Lie algebras and Lie groups.
We construct the first examples of manifolds, the simplest one being the product of S^3, S^4, and R^5, which admit infinitely many complete nonnegatively curved metrics with pairwise nonhomeomorphic souls.
Study on virtual knot groups and their lower central series properties.
Multitwists cannot generate all compactly supported mapping class groups on infinite-type surfaces.
The linear stability of warped product Einstein metrics as fixed points of the Ricci flow is investigated. We generalise the results of Gibbons, Hartnoll and Pope and show that in sufficiently low dimensions, all warped product Einstein metrics are unstable. By exploiting the relationship between warped product Einstei…
New insights into mapping class groups' cohomology.
Cyclohedra are a well-known infinite familiy of finite-dimensional polytopes that can be constructed from centrally symmetric triangulations of even-sided polygons. In this article we introduce an infinite-dimensional analogue and prove that the group of symmetries of our construction is a semidirect product of a degre…
This paper explores topological aspects of index theory for infinite-dimensional manifolds.
Study chaotic behavior in homeomorphism groups of countable products of spaces.
New findings on group actions and stabilizers of infinite sets.
Bestvina and Feighn showed that a morphism S --> T between two simplicial trees that commutes with the action of a group G can be written as a product of elementary folding operations. Here a more general morphism between simplicial trees is considered, which allow different groups to act on S and T. It is shown that t…
In this paper we study obstructions to presentability by products for finitely generated groups. Along the way we develop both the concept of acentral subgroups, and the relations between presentability by products on the one hand, and certain geometric and measure or orbit equivalence invariants of groups on the other…
We prove that graph products constructed over infinite graphs with bounded clique number preserve finite asymptotic dimension. We also study the extent to which Dranishnikov's property C, and Dranishnikov and Zarichnyi's straight finite decomposition complexity are preserved by constructions such as unions, free produc…
We establish the existence of infinitely many complete metrics with constant scalar curvature on prescribed conformal classes on certain noncompact product manifolds. These include products of closed manifolds with constant positive scalar curvature and simply-connected symmetric spaces of noncompact or Euclidean type;…
We study the geometry of compact Lorentzian manifolds that admit a somewhere timelike Killing vector field, and whose isometry group has infinitely many connected components. Up to a finite cover, such manifolds are products (or amalgamated products) of a flat Lorentzian torus and a compact Riemannian (resp., lightlike…
Study the geometry of graph product extension graphs.
Study shows hyperbolic subgroups can be free products of surface and free groups.
Study shows certain infinite-ended groups are not quasi-isometrically rigid.
We survey some results and questions about free actions of infinite groups on products of spheres and euclidean spaces, and give some new co-compact examples.
The paper explores idempotents in quandle rings and their connections to quandle coverings.
We consider a category whose morphisms are bordisms of -dimensional pseudomanifolds equipped with a certain additional structure (coloring). On the other hand, we consider the product of copies of infinite symmetric group. We show that unitary representations of produce functors from the category of …
We show that uniformly finite homology of products of trees vanishes in all degrees except degree , where it is infinite dimensional. Our method is geometric and applies to several large scale homology theories, including almost equivariant homology and controlled coarse homology. As an application we determine …
Study gradient Yamabe solitons on warped product manifolds.
Constructs an analytic index for infinite dimensional manifolds with -action.
The paper proves an infinite product identity on the Teichmüller space of a once-punctured torus.
Classifies totally geodesic submanifolds in symmetric spaces.