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.
The paper explores representations of graph manifolds to Seifert motion groups.
Paper introduces Manifold Probe for discovering representation manifolds in superposition.
New representations of hyperbolic 3-manifold groups into larger groups.
MKA incorporates manifold geometry into kernel alignment for more robust representation comparison.
Proves EGF representations in specific geometric contexts.
Study on hyperconvex representations of hyperbolic groups in complex flag manifolds.
The paper proves a quadratic formality for Sasakian manifolds' representation varieties.
Researchers calculate the volume of Seifert representations for graph manifolds and their covers.
Quantum theory uses modular group representations to assign invariants to 3-manifolds.
Anosov representations of surface groups are complex manifolds.
3-manifold groups can only have convex co-compact representations if they are geometric or hyperbolic.
We show that for a representation of the fundamental group of a triangulated closed 3-manifold (not necessarily hyperbolic) into $\PSL$ so that any edge loop has non-trivial image under the representation, there exist uncountably many solutions to the hyperbolic gluing equation whose associated representations are conj…
We construct projective unitary representations of the smooth Deligne cohomology group of a compact oriented Riemannian manifold of dimension 4k+1, generalizing positive energy representations of the loop group of the circle. We also classify such representations under a certain condition. The number of the equivalence…
New model allows sparse graphs with many triangles to be represented.
The Ptolemy coordinates for boundary-unipotent SL(n,C)-representations of a 3-manifold group were introduced in Garoufalidis-Thurston-Zickert inspired by the A-coordinates on higher Teichmüller space due to Fock and Goncharov. In this paper, we define the Ptolemy field of a (generic) PSL(2,\C)-representation and prove …
We show that the Thurston norm of any irreducible 3-manifold can be detected using twisted Reidemeister torsions corresponding to integral representations and also corresponding to representations over finite fields. In particular our result holds for all graph manifolds, these are not covered by the earlier work of th…
Study partially hyperbolic flows on flat bundles, proving equivalence for complete affine manifolds.
The theory of flat Pseudo-Riemannian manifolds and flat affine manifolds is closely connected to the topic of prehomogeneous affine representations of Lie groups. In this article, we exhibit several aspects of this correspondence. At the heart of our presentation is a development of the theory of characteristic classes…
Graph manifolds with small homology have non-trivial SU(2) representations.
New polynomial connects knot genus to 3-manifold geometry.
Manifold learning seeks a low dimensional representation that faithfully captures the essence of data. Current methods can successfully learn such representations, but do not provide a meaningful set of operations that are associated with the representation. Working towards operational representation learning, we endow…
A new class of 3-manifold invariants is constructed from representations of the category of framed tangles.
Study domination between non-Fuchsian surface group representations and anti-de Sitter geometry.
We prove universality theorems ("Murphy's Laws") for representation schemes of fundamental groups of closed 3-dimensional manifolds. We show that germs of SL(2,C)-representation schemes of such groups are essentially the same as germs of schemes of over rational numbers.
Introduces holed cone structures to generalize cone structures on 3-manifolds.
Linear representations help embed manifolds into matrix spaces.
A new method for representation and metric learning on manifolds boosts performance.
For a compact 3-manifold M with arbitrary (possibly empty) boundary, we give a parametrization of the set of conjugacy classes of boundary-unipotent representations of the fundamental group of M into SL(n,C). Our parametrization uses Ptolemy coordinates, which are inspired by coordinates on higher Teichmueller spaces d…
The first time that the connection between isometric immersion of surfaces and solutions of the Dirac equation appeared in the literature was in the seminal paper of Thomas Friedrich in 1998. In consequence of that, several authors contributed to this topic hereafter, by obtaining the spinorial representation of Spin m…
We consider the relationship between hyperbolic cone-manifold structures on surfaces, and algebraic representations of the fundamental group into a group of isometries. A hyperbolic cone-manifold structure on a surface, with all interior cone angles being integer multiples of , determines a holonomy representation …
The paper studies binary icosahedral representations of hyperbolic 3-manifolds.
Extends Fried's result to arbitrary representations of compact hyperbolic manifolds.
New CR representations are found and shown to be redundant.
This paper investigates how data augmentation improves linear separation of manifold data.
Semi-supervised learning algorithms typically construct a weighted graph of data points to represent a manifold. However, an explicit graph representation is problematic for neural networks operating in the online setting. Here, we propose a feed-forward neural network capable of semi-supervised learning on manifolds w…
Let M be a non-compact hyperbolic 3-manifold that has a triangulation by positively oriented ideal tetraedra. We explain how to produce local coordinates for the variety defined by the gluing equations for PGL(3,C)-representations. In particular we prove local rigidity of the "geometric" representation in PGL(3,C), rec…
GeoERM learns shared representations on Riemannian manifolds for multi-task learning.
New proof shows certain 3D shapes can't be instanton L-spaces.
Given a finite volume hyperbolic 3-manifold, we compose a lift of the holonomy in SL(2,C) with the n-dimensional irreducible representation of SL(2,C) in SL(n,C). In this paper we give local coordinates of the SL(n,C)-character variety around this representation. As a corollary, this representation is isolated among al…
The paper introduces a new geometric representation for data.
We present a signal representation framework called the sparse manifold transform that combines key ideas from sparse coding, manifold learning, and slow feature analysis. It turns non-linear transformations in the primary sensory signal space into linear interpolations in a representational embedding space while maint…
We prove a volume-rigidity theorem for fuchsian representations of fundamental groups of hyperbolic k-manifolds into Isom(H^n). Namely, we show that if M is a complete hyperbolic k-manifold with finite volume, then the volume of any representation of its fundamental group into Isom(H^n), 3 <= k <= n, is less than the v…
We consider the relationship between hyperbolic cone-manifold structures on surfaces, and algebraic representations of the fundamental group into a group of isometries. A hyperbolic cone-manifold structure on a surface, with all interior cone angles being integer multiples of , determines a holonomy representation …
Let M a 3-manifold with torus boundary which is a rational homology circle. We study deformations of reducible representations of p_1(M) into PSL_2(C) associated to a simple zero of the twisted Alexander polynomial. We also describe the local structure of the representation and character varieties.
We study low-dimensional representations of matrix groups over general rings, by considering group actions on CAT(0) spaces, spheres and acyclic manifolds.
We give an efficient simplicial formula for the volume and Chern-Simons invariant of a boundary-parabolic PSL(2,C)-representation of a tame 3-manifold. If the representation is the geometric representation of a hyperbolic 3-manifold, our formula computes the volume and Chern-Simons invariant directly from an ideal tria…
We study the topology and geometry of compact complex manifolds associated to Anosov representations of surface groups and other hyperbolic groups in a complex semisimple Lie group . These manifolds are obtained as quotients of the domains of discontinuity in generalized flag varieties constructed by Kapovich-…
A Dehn sphere in a closed 3-manifold M is a 2-sphere immersed in M with only double curve and triple point singularities. The Dehn sphere S fills M if it defines a cell-decomposition of M. The inverse image in S^{2} of the double curves of S is the Johansson diagram of S and if S fills M it is possible to reconstruct M…