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.
Graph potentials link to topological QFTs, with computational methods.
This paper proposes an axiomatic for Cyclic Foam Topological Field theories. That is Topological Field theories, corresponding to String theories, where particles are arbitrary graphs. World surfaces in this case are two-manifolds with one-dimensional singularities. We proved that Cyclic Foam Topological Field theories…
Polynomial algorithm found for alternating link equivalence.
We establish a relation between the trace evaluation in SO(3) topological quantum field theory and evaluations of a topological Tutte polynomial. As an application, a generalization of the Tutte golden identity is proved for graphs on the torus.
We consider the extension of classical 2-dimensional topological quantum field theories to Klein topological quantum field theories which allow unorientable surfaces. We approach this using the theory of modular operads by introducing a new operad governing associative algebras with involution. This operad is Koszul an…
This paper refines understanding of decentralized learning by considering graph topology.
New technique connects graph matching complexes to Morse theory for better topology understanding.
In these lecture notes we discuss a body of work in which Morse theory is used to construct various homology and cohomology operations. In the classical setting of algebraic topology this is done by constructing a moduli space of graph flows, using homotopy theoretic methods to construct a virtual fundamental class, an…
New TQFT homologies help color graphs, potentially solving the four color theorem.
Classifies graph configuration spaces homeomorphic to manifolds.
Graphs with given k vertices generate an (acyclic) simplicial complex. We describe the homology of its quotient complex, formed by all connected graphs, and demonstrate its applications to the topology of braid groups, knot theory, combinatorics, and singularity theory. The multidimensional analogues of this complex ar…
Paper categorifies a polynomial related to ribbon graphs.
Graph coloring is explained using a topological field theory with defects.
We first show that the braid group over a graph topologically containing no -shape subgraph has a presentation related only by commutators. Then using discrete Morse theory and triple Massey products, we prove that a graph topologically contains none of four prescribed graphs if and only if its 4-braid groups is a r…
Graphoids are topological invariants of virtual graph diagrams.
This work introduces a method to compare sparse neural network topologies using graph theory.
Well-quasi-orders proved on embedded planar graphs.
Classical knot theory can be generalized to virtual knot theory and spatial graph theory. In 2007, Fleming and Mellor combined virtual knot theory and spatial graph theory to form, combinatorially, virtual spatial graph theory. In this paper, we introduce a topological definition of virtual spatial graphs that is simil…
Quantum model for knotted graphs from knot theory.
This is a survey article for the forthcoming `A Concise Encyclopedia of Knot Theory.' We focus on the topology of spatial graphs with few vertices and edges, paying particular attention to Brunnian -graphs.
Paper describes a state sum formula for a graph coloring polynomial.
We extend the topological field theory (``itsy bitsy topological field theory"') of our previous work from mod-2 to twisted coefficients. This topological field theory is derived from sutured Floer homology but described purely in terms of surfaces with signed points on their boundary (occupied surfaces) and curves on …
One of the main questions in the theory of normal surface singularities is to understand the relations between their geometry and topology. The lattice cohomology is an important tool in the study of topological properties of a plumbed 3-manifold M associated with a connected negative definite plumbing graph G. It conn…
This is a glossary of notions and methods related with the topological theory of collections of affine planes, including braid groups, configuration spaces, order complexes, stratified Morse theory, simplicial resolutions, complexes of graphs, Orlik--Solomon rings, Salvetti complex, matroids, Spanier--Whitehead duality…
Graph manifolds with small homology have non-trivial SU(2) representations.
Paper presents voxel graph operators for vector data models.
PiNGDA learns beneficial noise for graph augmentation stability.
AdaCGP learns dynamic graph topology from time series data, improving over existing methods.
The topological Tverberg theorem has been generalized in several directions by setting extra restrictions on the Tverberg partitions. Restricted Tverberg partitions, defined by the idea that certain points cannot be in the same part, are encoded with graphs. When two points are adjacent in the graph, they are not in th…
This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions of 'quantum invariants' of manifolds inspired by ideas originating from physics.…
Proposes a probabilistic framework for stationary topological signals on simplicial complexes.
The paper introduces a quantum state system to count perfect matchings in graphs.
Consider a finite, regular cover of finite graphs, with associated deck group . We relate the topology of the cover to the structure of as a -representation. A central object in this study is the {\em primitive homology} group $H_1^{\mathrm{prim}}(Y;\mathbb{C})\subseteq H_1(Y;\mathbb{…
Extends knotoid theory to include multiple poles and intervals.
We solve Euler equations on graph manifolds, classifying steady flows with Morse-Bott Bernoulli functions.
New topological realization of Kontsevich graph complex for large dimensions.
The curve graph's model theory reveals its central role in surface study.
Solved Cheeger inequalities for simplicial complexes, combining topological and graph theoretic methods.
New framework for 3D spatial topology enumeration and identification.
Researchers identify graph components for unicellular collections.
New model learns from random graph samples to estimate graph parameters.
Graph convolutional networks (GCNs) are powerful tools for graph-structured data. However, they have been recently shown to be vulnerable to topological attacks. To enhance adversarial robustness, we go beyond spectral graph theory to robust graph theory. By challenging the classical graph Laplacian, we propose a new c…
The paper generalizes virtual knot theory using multiple types of virtual crossings.
This paper develops a discrete theory of real Riemann surfaces using quad-graphs and linear discretization.
Lecture notes on crystallography and discrete surfaces.
The paper explores invariants of graph drawings in the plane.
This article is an exposition of a body of existing results, together with an announcement of recent results. We discuss a theory of polytopes associated to bipartite graphs and trinities, developed by Kálmán, Postnikov and others. This theory exhibits a variety of interesting duality and triality relations, and extend…
Given a smooth closed manifold M with a family {L_i} of closed submanifolds, we consider the free loop space LM and the spaces PM(L_i,L_j) of open strings (paths g:[0,1]->M with g(0) in L_i, and g(1) in L_j). We construct string topology operations resulting in an open-closed TQFT on the family (h_*(LM),h_*(PM(L_i,L_j)…