scholarly journals Virtual 1-domination of 3-manifolds

2018 ◽  
Vol 154 (3) ◽  
pp. 621-639 ◽  
Author(s):  
Yi Liu ◽  
Hongbin Sun
Keyword(s):  
Finite Cover

It is shown in this paper that given any closed oriented hyperbolic 3-manifold, every closed oriented 3-manifold is mapped onto by a finite cover of that manifold via a map of degree 1, or in other words, virtually 1-dominated by that manifold. This improves a known result of virtual 2-domination. The proof invokes a recently developed enhanced version of the connection principle in good pants constructions.

scholarly journals Revisiting Leighton’s theorem with the Haar measure

2020 ◽  
pp. 1-9
Author(s):  
DANIEL J. WOODHOUSE
Keyword(s):  
Haar Measure ◽  
Free Groups ◽  
Finite Cover ◽  
Covering Theorem ◽  
Rigidity Result ◽  
Graph Covering ◽  
Finite Graphs ◽  
Universal Covers ◽  
Line Patterns

Abstract Leighton’s graph covering theorem states that a pair of finite graphs with isomorphic universal covers have a common finite cover. We provide a new proof of Leighton’s theorem that allows generalisations; we prove the corresponding result for graphs with fins. As a corollary we obtain pattern rigidity for free groups with line patterns, building on the work of Cashen–Macura and Hagen–Touikan. To illustrate the potential for future applications, we give a quasi-isometric rigidity result for a family of cyclic doubles of free groups.

scholarly journals DEVELOPMENT OF FRACTURE SIMULATION BY THE FINITE COVER METHOD USING INTERFACE ELEMENT

2005 ◽  
pp. 213-225 ◽  
Author(s):  
Tateki ISHII ◽  
Kenjiro TERADA ◽  
Takashi KYOYA ◽  
Yuji KISHINO
Keyword(s):  
Interface Element ◽  
Finite Cover ◽  
Fracture Simulation ◽  
Finite Cover Method

Pseudo-finite homogeneity and saturation

1999 ◽  
Vol 64 (4) ◽  
pp. 1689-1699 ◽  
Author(s):  
Jörg Flum ◽  
Martin Ziegler
Keyword(s):  
Expressive Power ◽  
Query Languages ◽  
Stable Theory ◽  
Finite Cover ◽  
Database Query ◽  
Homogeneity Property ◽  
Finite States

AbstractWhen analyzing database query languages a roperty, of theories, the pseudo-finite homogeneity property, has been introduced and applied (cf. [3]). We show that a stable theory has the pseudo-finite homogeneity property just in case its expressive power for finite states is bounded. Moreover, we introduce the corresponding pseudo-finite saturation property and show that a theory fails to have the finite cover property if and only if it has the pseudo-finite saturation property.

904 Improvement of accuracy in finite cover method by mesh superposition method

2005 ◽  
Vol 2005.18 (0) ◽  
pp. 177-178
Author(s):  
Katsuyuki SUZUKI ◽  
Shogo NAKASUMI ◽  
Toshifumi SHIMAMURA
Keyword(s):  
Superposition Method ◽  
Finite Cover ◽  
Finite Cover Method

scholarly journals DMP in strongly minimal sets

2007 ◽  
Vol 72 (3) ◽  
pp. 1019-1030 ◽  
Author(s):  
Assaf Hasson ◽  
Ehud Hrushovski
Keyword(s):  
Finite Cover ◽  
Minimal Set ◽  
Minimal Sets ◽  
Minimal Theory

AbstractWe construct a strongly minimal set which is not a finite cover of one with DMP. We also show that for a strongly minimal theory T, generic automorphisms exist iff T has DMP, thus proving a conjecture of Kikyo and Pillay.

On the weak non-finite cover property and the n-tuples of simple structures

2005 ◽  
Vol 70 (1) ◽  
pp. 235-251 ◽  
Author(s):  
Evgueni Vassiliev
Keyword(s):  
Direct Proof ◽  
Simple Theory ◽  
Finite Cover ◽  
Stable Case ◽  
Combinatorial Condition ◽  
The Way

AbstractThe weak non-finite cover property (wnfcp) was introduced in [1] in connection with “axiomatizability” of lovely pairs of models of a simple theory. We find a combinatorial condition on a simple theory equivalent to the wnfcp, yielding a direct proof that the non-finite cover property implies the wnfcp, and that the wnfcp is preserved under reducts. We also study the question whether the wnfcp is preserved when passing from a simple theory T to the theory Tp of lovely pairs of models of T (true in the stable case). While the question remains open, we show, among other things, that if (for a T with the wnfcp) Tp is low, then TP has the wnfcp. To study this question, we describe “double lovely pairs”, and, along the way, we develop the notion of a “lovely n-tuple” of models of a simple theory, which is an analogue of the notion of a beautiful tuple of models of stable theories [2].

scholarly journals Semistable reduction for overconvergent F-isocrystals, IV: local semistable reduction at nonmonomial valuations

2011 ◽  
Vol 147 (2) ◽  
pp. 467-523 ◽  
Author(s):  
Kiran S. Kedlaya
Keyword(s):  
Positive Characteristic ◽  
Degree Zero ◽  
Local Problem ◽  
Finite Cover ◽  
Semistable Reduction ◽  
Numerical Invariants ◽  
Rational Rank ◽  
Logarithmic Singularities ◽  
Meromorphic Connection ◽  
Field Of Positive Characteristic

AbstractWe complete our proof that given an overconvergent F-isocrystal on a variety over a field of positive characteristic, one can pull back along a suitable generically finite cover to obtain an isocrystal which extends, with logarithmic singularities and nilpotent residues, to some complete variety. We also establish an analogue for F-isocrystals overconvergent inside a partial compactification. By previous results, this reduces to solving a local problem in a neighborhood of a valuation of height 1 and residual transcendence degree zero. We do this by studying the variation of some numerical invariants attached to p-adic differential modules, analogous to the irregularity of a complex meromorphic connection. This allows for an induction on the transcendence defect of the valuation, i.e., the discrepancy between the dimension of the variety and the rational rank of the valuation.

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