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 surgery exact triangles in Heegaard Floer homology for rational slopes.
Graphlets are defined as k-node connected induced subgraph patterns. For an undirected graph, 3-node graphlets include close triangle and open triangle. When k = 4, there are six types of graphlets, e.g., tailed-triangle and clique are two possible 4-node graphlets. The number of each graphlet, called graphlet count, i…
SU(3) instanton homology counts Tait colorings for webs and foams.
New deformations of lattice cohomology help calculate knot invariants.
We consider the problem of the combinatorial computation of the first Chern class of a circle bundle. N.Mnev found such a formula in terms of canonical shellings. It represents certain invariant of a triangulation computed by analyzing cyclic word in 3-character alphabet associated to the bundle. This curvature is a ki…
We construct a spectral sequence from the reduced odd Khovanov homology of a link converging to the framed instanton homology of the double cover branched over the link, with orientation reversed. Framed instanton homology counts certain instantons on the cylinder of a 3-manifold connect-summed with a 3-torus. En route…
This is an expository paper designed to introduce undergraduates to the Atiyah-Singer index theorem 50 years after its announcement. It includes motivation, a statement of the theorem, an outline of the easy part of the heat equation proof. It includes counting lattice points and knot concordance as applications.
The paper computes special values of combinatorial zeta functions to reveal topological properties of manifolds.
We show that the bordered-sutured Floer invariant of the complement of a tangle in an arbitrary 3-manifold , with minimal conditions on the bordered-sutured structure, satisfies an unoriented skein exact triangle. This generalizes a theorem by Manolescu for links in . We give a theoretical proof of this result …
To capture the inherent geometric features of many community detection problems, we propose to use a new random graph model of communities that we call a Geometric Block Model. The geometric block model generalizes the random geometric graphs in the same way that the well-studied stochastic block model generalizes the …
Exploratory analysis over network data is often limited by the ability to efficiently calculate graph statistics, which can provide a model-free understanding of the macroscopic properties of a network. We introduce a framework for estimating the graphlet count---the number of occurrences of a small subgraph motif (e.g…
This is the first in a series of papers exploring the relationship between the Rohlin invariant and gauge theory. We discuss the Casson-type invariant of a 3-manifold with the integral homology of a torus, given by counting projectively flat connections. We show that its mod 2 evaluation is given by the triple cup prod…
odeN efficiently approximates multiple temporal motifs in large networks.
We show a connection between a surgery exact sequence in knot Floer homology and the sequence derived in [18]. As a consequence of this relationship we see that the exact sequence in [18] also works with coherent orientations and admits refinements with respect to spinc-structures. As an application of this discussion,…
Stochastic Kronecker graphs supply a parsimonious model for large sparse real world graphs. They can specify the distribution of a large random graph using only three or four parameters. Those parameters have however proved difficult to choose in specific applications. This article looks at method of moments estimators…
Lipshitz, Ozsváth and Thurston defined a bordered Heegaard Floer invariant CFDA for 3-manifolds with two boundary components, including mapping cylinders for surface diffeomorphisms. We define a related invariant for certain 4-dimensional cobordisms with corners, by associating a morphism F from CFDA(f) to CFDA(g) to e…
This article introduces an application of Ghrist barcodes in the study of persistent Betti numbers derived from vortex nerve complexes found in triangulations of video frames. A Ghrist barcode is a topology of data pictograph useful in representing the persistence of the features of changing shapes. The basic approach …
Napoleonic triangles don't exist in hyperbolic geometry.
New bounds on inscribed triangles in arbitrary planar domains.
Paper calculates eigenvalues of a specific triangle on a sphere.
Study on Laplacian determinant in isosceles triangles, finding equilateral triangle minimizes determinant.
CSNE embeds signed networks by separating structural and fine-grained information.
New method shows any triangle group generating pair is related to special coverings.
Complex hyperbolic triangle groups were first considered by Mostow in building the first nonarithmetic lattices in PU(2, 1). They are a natural generalization of the classical triangle groups acting on the hyperbolic plane. A well-known theorem of Takeuchi is that there are only finitely many Fuchsian triangle groups t…
Defines band maps in unoriented link Floer homology forming a skein exact triangle.
Proves a new skein exact triangle for real monopole Floer homology.
The study counts triangulations of a projective plane with specific vertex valencies.
We answer the question "Does the Y-triangle move preserve intrinsic knottedness?" in the negative by giving an example of a graph that is obtained from the intrinsically knotted graph K_7 by triangle-Y and Y-triangle moves but is not intrinsically knotted.
Study calculates eigenvalues and eigenfunctions for spherical triangles and finds fundamental gap behavior.
We show that the triangle with angles Pi/12, Pi/3 and 7*Pi/12 has the lattice property and compute this triangle's Veech group.
We study side-lengths of triangles in path metric spaces. We prove that unless such a space X is bounded, or quasi-isometric to line or half-line, every triple of real numbers satisfying the strict triangle inequalities, is realized by the side-lengths of a triangle in X. We construct an example of a complete path metr…
Two triples of triangles having pairwise disjoint outlines in 3-space are called combinatorially isotopic if one triple can be obtained from the other by a continuous motion during which the outlines of the triangles remain pairwise disjoint. We conjecture that it can be algorithmically checked if an (ordered or unorde…
New method proves mateability of triangle groups with Blaschke products.
In this paper we study the area of ideals triangles in a convex domain with its Hilbert geometry. We obtain a characterization of the hyperbolic geometry among all the Hilbert geometry in terms of area of ideals triangles. We also obtain a sharp lower bound on the hilbert area of ideal triangles, independant of the con…
This article introduces planar ribbons, Vergili ribbon complexes and ribbon nerves in Alexandroff-Hopf-Whitehead CW (Closure finite Weak) topological spaces. A {\em planar ribbon} (briefly, {ribbon}) in a CW space is the closure of a pair of nesting, non-concentric filled cycles that includes the boundary but does not …
In Lorentzian geometry, limited definition of angles restricts the use of angle bisectors in study of triangles. This paper redefines angle bisectors so that they can be used to study attributes of triangles. Using the new definition, this paper investigates the existence of the incenter and the isogonal conjugate of a…
A formula for Rademacher symbols in triangle groups is provided.
Study stabilizers of complex hyperbolic triangle groups, finding generators and signatures.
Criterion for stopping conjugacy class enumeration in triangle groups.
New skein exact triangles for link Floer homology.
New theorem disproves Angle Defect for super triangles.
The study examines Lipschitz normally embedded Hölder triangles in 4D space.
Triangle Artin groups split as graphs of free groups under specific conditions.
The paper finds extremum values for mixed Laplacian eigenvalues on triangles and trapezoids.
Study on 3D surfaces and tangles formed by Poncelet triangles.
Study of subgroups in complex hyperbolic lattice triangle groups.
Triangle groups uniquely identified by their finite quotients.
Study orbits in right triangles, deducing periodic billiard paths and classifying orbit closures.