Finite covers of N0-categorical structures

2019 ◽  
pp. 75-86
Author(s):  
David M. Evans
Keyword(s):  
Finite Covers

scholarly journals Permutation groups with small orbit growth

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Manuel Bodirsky ◽  
Bertalan Bodor
Keyword(s):  
Automorphism Group ◽  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Permutation Groups ◽  
First Order ◽  
Finite Covers

Abstract Let K exp + \mathcal{K}_{{\operatorname{exp}}{+}} be the class of all structures 𝔄 such that the automorphism group of 𝔄 has at most c ⁢ n d ⁢ n cn^{dn} orbits in its componentwise action on the set of 𝑛-tuples with pairwise distinct entries, for some constants c , d c,d with d < 1 d<1 . We show that K exp + \mathcal{K}_{{\operatorname{exp}}{+}} is precisely the class of finite covers of first-order reducts of unary structures, and also that K exp + \mathcal{K}_{{\operatorname{exp}}{+}} is precisely the class of first-order reducts of finite covers of unary structures. It follows that the class of first-order reducts of finite covers of unary structures is closed under taking model companions and model-complete cores, which is an important property when studying the constraint satisfaction problem for structures from K exp + \mathcal{K}_{{\operatorname{exp}}{+}} . We also show that Thomas’ conjecture holds for K exp + \mathcal{K}_{{\operatorname{exp}}{+}} : all structures in K exp + \mathcal{K}_{{\operatorname{exp}}{+}} have finitely many first-order reducts up to first-order interdefinability.

scholarly journals Constructing 1-cusped isospectral non-isometric hyperbolic 3-manifolds

2017 ◽  
Vol 10 (01) ◽  
pp. 1-25
Author(s):  
Stavros Garoufalidis ◽  
Alan W. Reid
Keyword(s):  
Discrete Spectrum ◽  
Eisenstein Series ◽  
Finite Volume ◽  
Finite Covers ◽  
Figure Eight Knot ◽  
Complex Length

We construct infinitely many examples of pairs of isospectral but non-isometric [Formula: see text]-cusped hyperbolic [Formula: see text]-manifolds. These examples have infinite discrete spectrum and the same Eisenstein series. Our constructions are based on an application of Sunada’s method in the cusped setting, and so in addition our pairs are finite covers of the same degree of a 1-cusped hyperbolic 3-orbifold (indeed manifold) and also have the same complex length spectra. Finally we prove that any finite volume hyperbolic 3-manifold isospectral to the figure-eight knot complement is homeomorphic to the figure-eight knot complement.

scholarly journals Deformation of finite morphisms and smoothing of ropes

2008 ◽  
Vol 144 (3) ◽  
pp. 673-688 ◽  
Author(s):  
Francisco Javier Gallego ◽  
Miguel González ◽  
Bangere P. Purnaprajna
Keyword(s):  
General Theory ◽  
Projective Space ◽  
General Result ◽  
The Other ◽  
Independent Interest ◽  
Higher Dimension ◽  
Smooth Curves ◽  
Other Hand ◽  
Finite Covers ◽  
The One

AbstractIn this paper we prove that most ropes of arbitrary multiplicity supported on smooth curves can be smoothed. By a rope being smoothable we mean that the rope is the flat limit of a family of smooth, irreducible curves. To construct a smoothing, we connect, on the one hand, deformations of a finite morphism to projective space and, on the other hand, morphisms from a rope to projective space. We also prove a general result of independent interest, namely that finite covers onto smooth irreducible curves embedded in projective space can be deformed to a family of 1:1 maps. We apply our general theory to prove the smoothing of ropes of multiplicity 3 on P1. Even though this paper focuses on ropes of dimension 1, our method yields a general approach to deal with the smoothing of ropes of higher dimension.

scholarly journals Nori fundamental gerbe of essentially finite covers and Galois closure of towers of torsors

2019 ◽  
Vol 25 (2) ◽  
Author(s):  
Marco Antei ◽  
Indranil Biswas ◽  
Michel Emsalem ◽  
Fabio Tonini ◽  
Lei Zhang
Keyword(s):  
Galois Closure ◽  
Finite Covers

scholarly journals Second cohomology groups and finite covers of infinite symmetric groups

2011 ◽  
Vol 330 (1) ◽  
pp. 221-233 ◽  
Author(s):  
David M. Evans ◽  
Elisabetta Pastori
Keyword(s):  
Symmetric Groups ◽  
Cohomology Groups ◽  
Finite Covers

Numerical Modeling of Fracture Process Using Element-Free Method

2013 ◽  
Vol 427-429 ◽  
pp. 146-149
Author(s):  
Cheng Fan
Keyword(s):  
Interpolation Method ◽  
Kriging Interpolation ◽  
Computational Accuracy ◽  
Simple Method ◽  
Solution Domain ◽  
Kriging Interpolation Method ◽  
Finite Covers ◽  
Crack Problems ◽  
Cover Systems ◽  
Element Free

A new element-free formulation of Kriging interpolation procedure based on finite covers technique and Kriging interpolation method which integrates the flexibilities of the manifold method in dealing with discontinuity and the element-free features of the moving Kriging interpolation. Two cover systems are employed in this method. Mathematical cover of the solution domain under consideration are used to construct shape function and physical cover is used to reproduce the geometry of the solution domain. The mathematical covers can take any types of shape and is much easily formed compared with those in the conventional MM. The presented method can overcome some difficulties in conventional element-free Galerkin methods in treating discontinuous crack problems. The fundamental theory of this procedure is illustrated and numerical analyses of examples show that the proposed procedure is an effective and simple method with higher computational accuracy.

scholarly journals The primitivity index function for a free group, and untangling closed curves on hyperbolic surfaces.With the appendix by Khalid Bou–Rabee

2017 ◽  
Vol 166 (1) ◽  
pp. 83-121
Author(s):  
NEHA GUPTA ◽  
ILYA KAPOVICH
Keyword(s):  
Lower Bounds ◽  
Free Group ◽  
Growth Function ◽  
Residual Finiteness ◽  
Closed Geodesics ◽  
Hyperbolic Surfaces ◽  
Finitely Generated ◽  
Closed Curves ◽  
Index Function ◽  
Finite Covers

AbstractMotivated by the results of Scott and Patel about “untangling” closed geodesics in finite covers of hyperbolic surfaces, we introduce and study primitivity, simplicity and non-filling index functions for finitely generated free groups. We obtain lower bounds for these functions and relate these free group results back to the setting of hyperbolic surfaces. An appendix by Khalid Bou–Rabee connects the primitivity index functionfprim(n,FN) to the residual finiteness growth function forFN.

scholarly journals Indiscriminate covers of infinite translation surfaces are innocent, not devious

2017 ◽  
Vol 39 (8) ◽  
pp. 2071-2127 ◽  
Author(s):  
W. PATRICK HOOPER ◽  
RODRIGO TREVIÑO
Keyword(s):  
Topological Type ◽  
Translation Surfaces ◽  
Finite Area ◽  
Infinite Type ◽  
Ergodic Properties ◽  
Finite Covers ◽  
Straight Line ◽  
Line Flow ◽  
Natural Notion ◽  
The Relationship

We consider the interaction between passing to finite covers and ergodic properties of the straight-line flow on finite-area translation surfaces with infinite topological type. Infinite type provides for a rich family of degree-$d$ covers for any integer $d>1$. We give examples which demonstrate that passing to a finite cover can destroy ergodicity, but we also provide evidence that this phenomenon is rare. We define a natural notion of a random degree $d$ cover and show that, in many cases, ergodicity and unique ergodicity are preserved under passing to random covers. This work provides a new context for exploring the relationship between recurrence of the Teichmüller flow and ergodic properties of the straight-line flow.

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