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.
Study Kazdan-Warner equations on graphs using Brouwer degree theory.
The paper calculates the slicing degree of knots using advanced homology theories.
Proves rigidity for maps between manifolds using degree theory and current developments.
String structures in degree four are associated with cancellation of anomalies of string theory in ten dimensions. Fivebrane structures in degree eight have recently been shown to be associated with cancellation of anomalies associated to the NS5-brane in string theory as well as the M5-brane in M-theory. We introduce …
In [3] Borzellino and Brunsden started to develop an elementary differential topology theory for orbifolds. In this paper we carry on their project by defining a mapping degree for proper maps between orbifolds, which counts preimages of regular values with appropriate weights. We show that the mapping degree satisfies…
New degree theory proves existence of solitons on 4D manifolds.
Introduces quadratic linking degree in algebraic geometry.
New algebraic theory classifies symplectic curves in complex projective space.
The paper explores the index theory of sub-Laplacians on higher nilpotent Carnot manifolds.
This paper finds all prime alternating knots with minimal warping degree two.
The aim of this paper is twofold. On the one hand, it provides a review of the links between random tensor models, seen as quantum gravity theories, and the PL-manifolds representation by means of edge-colored graphs (crystallization theory). On the other hand, the core of the paper is to establish results about the to…
Study on knots formed by gluing ellipses, defining gluing degree.
Degree one twisting of Deligne cohomology, as a differential refinement of integral cohomology, was established in previous work. Here we consider higher degree twists. The Rham complex, hence de Rham cohomology, admits twists of any odd degree. However, in order to consider twists of integral cohomology we need a peri…
We develop the theory of equivariant harmonic self-maps of compact cohomogeneity one manifolds and construct new harmonic self-maps of the compact Lie groups SO(4L+2), L >= 1, with degree -3, of SO(8), SO(14) and SO(26) with degree -5 each, of SO(10) with degree -7, and of SO(14) with degree -11 by exhibiting linear so…
We develop a degree theory for compact immersed hypersurfaces of prescribed -curvature immersed in a compact, orientable Riemannian manifold, where is any elliptic curvature function. We apply this theory to count the (algebraic) number of immersed hyperspheres in various cases: where is mean curvature; extr…
Deep learning explained through spectral filtering of hierarchical features.
The study finds lower bounds for the warping degree of a knot projection.
Develops differential KO-character to determine real vector bundles in multiples of 8.
A new simple proof for surface map degree inequality.
Paper extends circle pattern theory to obtuse angles.
We demonstrate the equivalence of all loop closed topological string amplitudes on toric local Calabi-Yau threefolds with computations of certain knot invariants for Chern-Simons theory. We use this equivalence to compute the topological string amplitudes in certain cases to very high degree and to all genera. In parti…
We prove in this paper that, under suitable coinditions on an initial data set, we can obtain Area and Curvature Estimates for simple marginally outer trapped surfaces (or MOTS). Using this estimates, we derive a Compactness Theorem for MOTS. Moreover, the Compactness Theorem will allow us to adapt the recent Degree Th…
First the title could be also understood as ``3-manifolds related by non-zero degree maps" or "Degrees of maps between 3-manifolds" for some aspects in this survey talk. The topology of surfaces was completely understood at the end of 19th century, but maps between surfaces kept to be an active topic in the 20th centur…
Expander graphs have been a focus of attention in computer science in the last four decades. In recent years a high dimensional theory of expanders is emerging. There are several possible generalizations of the theory of expansion to simplicial complexes, among them stand out coboundary expansion and topological expand…
Curves with constant torsion can be deformed arbitrarily.
We prove that a reduced and irreducible algebraic surface in containing infinitely many twistor lines cannot have odd degree. Then, exploiting the theory of quaternionic slice regularity and the normalization map of a surface, we give constructive existence results for even degrees.
A formula for the difference of Vassiliev invariants of degree k+1 of two knots all of whose Vassiliev invariants of degree k agree is proven. The proof uses K. Habiro's C-moves and his theorem which relates them to Vassiliev invariants.
Enhances psyquandle invariants for singular and pseudoknots.
Paper studies Hessian quotient equations in warped product manifolds.
Topological degrees of continuous mappings between manifolds of even dimension are studied in terms of index theory of pseudo-differential operators. The index formalism of non-commutative geometry is used to derive analytic integral formulas for the index of a 0:th order pseudo-differential operator twisted by a Hölde…
Lower bound on minimum vertex degree for non-negative Lin-Lu-Yau curvature on graphs.
Solves Demailly's system for direct sums of ample line bundles on Riemann surfaces.
We use invariants of Hendricks and Manolescu coming from involutive Heegaard Floer theory to find constraints on possible configurations of singular points of a rational cuspidal curve of odd degree in the projective plane. We show that the results do not carry over to rational cuspidal curves of even degree.
(d+1)-colored graphs, i.e. edge-colored graphs that are (d+1)-regular, have already been proved to be a useful representation tool for compact PL d-manifolds, thus extending the theory (known as crystallization theory) originally developed for the closed case. In this context, combinatorially defined PL invariants play…
Extends residue theory to flags of holomorphic distributions.
The classical Hurwitz numbers of degree n together with the Hurwitz numbers of the seamed surfaces of degree n give rise to the Klein topological field theory. We extend this construction to the Hurwitz numbers of all degrees at once. The corresponding Cardy-Frobenius algebra is induced by arbitrary Young diagrams and …
The paper studies unknotting operations and numbers for plus-welded knotoids.
Introduces a new price measure and a second-order economic theory for volatility forecasting.
Affine cactus groups are CAT(0) and hyperbolic.
Notes on quasiregular maps between Riemannian manifolds, preserving Sobolev forms.
We show a non-existence result for some class of equivariant maps between sphere bundles over tori. The notion of equivariant KO-degree is used in the proof. As an application to Seiberg-Witten theory, for a connected closed oriented spin 4-manifold with indefinite intersection form, we have a new bound of the second B…
Alexander polynomial degree correlates with knot defect, proving conjecture for defect zero.
Study shows no hidden symmetries in specific spacetime metrics.
The entropy-degree theorem applies to Alexandrov spaces with curvature constraints.
The notion of a higher bundle gerbe is introduced to give a geometric realization of the higher degree integral cohomology of certain manifolds. We consider examples using the infinite dimensional spaces arising in gauge theories.
As nilpotent studies in knot theory, we focus on invariants of Milnor, Orr, and Kontsevich. We show that the Orr invariant of degree is equivalent to the tree reduction of the Kontsevich invariant of degree . Furthermore, we will see a close relation between the Orr invariant and the Milnor invariant, and …
The number of BMW groups on tree products is bounded.
The notion of topological degree is studied for mappings from the boundary of a relatively compact strictly pseudo-convex domain in a Stein manifold into a manifold in terms of index theory of Toeplitz operators on the Hardy space. The index formalism of non-commutative geometry is used to derive analytic integral form…