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.
Constructs a model for differential KO-theory using Clifford modules.
We provide several constructions in differential KO-theory. First, we construct a differential refinement of the -genus and a pushforward leading to a Riemann-Roch theorem. We set up a differential refinement of the Atiyah-Hirzebruch spectral sequence (AHSS) for differential KO-theory and explicitly identify t…
Study pin manifolds using Clifford linear Dirac operator and KO-theory.
Develops differential KO-character to determine real vector bundles in multiples of 8.
We provide a systematic approach to twisting differential KO-theory leading to a construction of the corresponding twisted differential Atiyah-Hirzebruch spectral sequence (AHSS). We relate and contrast the degree two and the degree one twists, whose description involves appropriate local systems. Along the way, we pro…
The main new result here is the cancellation of global anomalies in the Type I superstring, with and without D-branes. Our argument here depends on a precise interpretation of the 2-form abelian gauge field using KO-theory; then the anomaly cancellation follows from a geometric form of the full Atiyah-Singer index theo…
Using Seiberg-Witten Floer spectrum and Pin(2)-equivariant KO-theory, we prove new Furuta-type inequalities on the intersection forms of spin cobordisms between homology -spheres. As an application, we give explicit constrains on the intersection forms of spin -manifolds bounded by Brieskorn spheres $\pmΣ(2,3,6k\…
We give a geometric characterisation of the topological invariants associated to SO(m,m+1)-Higgs bundles through KO-theory and the Langlands correspondence between orthogonal and symplectic Hitchin systems. By defining the split orthogonal spectral data, we obtain a natural grading of the moduli space of SO(m,m+1)-Higg…
We establish a mod 2 index theorem for real vector bundles over 8k+2 dimensional compact pin manifolds. The analytic index is the reduced invariant of (twisted) Dirac operators and the topological index is defined through -theory. Our main result extends the mod 2 index theorem of Atiyan and Singer to non-o…
Doing surgery on the 5-torus, we construct a 5-dimensional closed spin-manifold M with , so that the index invariant in the KO-theory of the reduced -algebra of is zero. Then we use the theory of minimal surfaces of Schoen/Yau to show that this manifolds cannot carry a metric of pos…
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…
We present a cocycle model for elliptic cohomology with complex coefficients in which methods from 2-dimensional quantum field theory can be used to rigorously construct cocycles. For example, quantizing a theory of vector bundle-valued fermions yields a cocycle representative of the elliptic Thom class. This construct…
Researchers prove a method to upgrade Morse-Bott homology to stable homotopy invariants.
We study the effects of having multiple Spin structures on the partition function of the spacetime fields in M-theory. This leads to a potential anomaly which appears in the eta-invariants upon variation of the Spin structure. The main source of such spaces are manifolds with nontrivial fundamental group, which are als…
Unified classification of equivariant principal bundles using higher homotopy theory.
The closure conditions of the inexact exterior differential form and dual form (an equality to zero of differentials of these forms) can be treated as a definition of some differential-geometrical structure. Such a connection discloses the properties and specific features of the differential-geometrical structures. The…
Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for the existence of a complete uniform differential structure on a given differenti…
In this paper we give explicit formulas of differential characteristic classes of principal -bundles with connections and prove their expected properties. In particular, we obtain explicit formulas for differential Chern classes, differential Pontryagin classes and differential Euler class. Furthermore, we show that…
We define the Simons-Sullivan differential analytic index by translating the Freed-Lott differential analytic index via explicit ring isomorphisms between Freed-Lott differential K-theory and Simons-Sullivan differential K-theory. We prove the differential Grothendieck-Riemann-Roch theorem in Simons-Sullivan differenti…
We generalize stochastic smoothing for gradient estimation of non-differentiable functions.
The paper proves Gorenstein contractions for multiscale differentials on nodal curves.
Classifies components of strata of k-differentials on Riemann surfaces.
Monotonic differentiable sorting networks improve upon previous methods.
Lecture notes introduce differential geometry using sheaves and differential operators.
Given a unital associatve graded algebra we construct the graded q-differential algebra by means of a graded q-commutator, where q is a primitive N-th root of unity. The N-th power (N>1) of the differential of this graded q-differential algebra is equal to zero. We use our approach to construct the graded q-differentia…
Paper defines quasi-Strebel structures for meromorphic k-differentials and proves their existence.
Finite intersection numbers between horizontal foliations of quadratic differentials.
We give chain homotopy maps of Khovanov-type link homology of a universal differential. The universal differential, discussed by Mikhail Khovanov, Marco Mackaay, Paul Turner and Pedro Vaz, contains the original Khovanov's differential and Lee's differential. We also consider the conditions of any differential ensuring …
We consider differentiable maps in the setting of Abstract Differential Geometry and we study the conditions that ensure the uniqueness of differentials in this setting. In particular, we prove that smooth maps between smooth manifolds admit a unique differential, coinciding with the usual one. Thus smooth manifolds fo…
Paper solves a class of differential equations with specific solutions.
We develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a ring to the differential algebraic K-theory. We also treat some of the foundational aspects of differential cohomology, including differential function spectra a…
By adapting the Cheeger-Simons approach to differential cohomology, we establish a notion of differential cohomology with compact support. We show that it is functorial with respect to open embeddings and that it fits into a natural diagram of exact sequences which compare it to compactly supported singular cohomology …
We study two notions of relative differential cohomology, using the model of differential characters. The two notions arise from the two options to construct relative homology, either by cycles of a quotient complex or of a mapping cone complex. We discuss the relation of the two notions of relative differential cohomo…
In this paper we discuss the question of integrating differential graded Lie algebras (DGLA) to differential graded Lie groups (DGLG). We first recall the classical problem of integration in the context, and present the construction for (non-graded) differential Lie algebras. Then, we define the category of differentia…
New privacy framework tailored to specific data distributions.
Studies projective geometry and partial differential equations prolongation.
Develops differential K-theory for noncommutative algebras.
Extends differential geometry concepts to manifolds with super tangent bundles.
Generalized differential cohomology theories, in particular differential K-theory (often called "smooth K-theory"), are becoming an important tool in differential geometry and in mathematical physics. In this survey, we describe the developments of the recent decades in this area. In particular, we discuss axiomatic ch…
Differentiable pipeline replaces non-differentiable CAE components for shape optimization.
Differentiable programming aids in solving differential equations and their sensitivities.
The purpose of this paper is to connect two subjects: the theory of quantum integrable systems (complete commutative rings of differential operators), and differential Galois theory. We define quantum completely integrable systems (QCIS), algebraically integrable QCIS, the differential Galois group of a QCIS. We show t…
A brief introduction to exterior differential systems for graduate students familiar with manifolds and differential forms. For complete files, see https://github.com/Ben-McKay/introduction-to-exterior-differential-systems
DiffEqFlux.jl is a library for fusing neural networks and differential equations. In this work we describe differential equations from the viewpoint of data science and discuss the complementary nature between machine learning models and differential equations. We demonstrate the ability to incorporate DifferentialEqua…
Differential K-theory gets a -ring structure.
We study Cheeger-Simons differential characters and provide geometric descriptions of the ring structure and of the fiber integration map. The uniqueness of differential cohomology (up to unique natural transformation) is proved by deriving an explicit formula for any natural transformation between a differential cohom…
Defines semi-symmetric metric connections on differential forms.
In this paper we first prove that every differential character can be represented by differential form with singularities. Then we lift the Gauss-Bonnet-Chern theorem for vector bundles to differential characters.