scholarly journals Simple connectivity of Fargues–Fontaine curves

2021 ◽  
Vol 4 ◽  
pp. 1203-1233
Author(s):  
Kiran S. Kedlaya
Keyword(s):  
Simple Connectivity

scholarly journals Topology of random -dimensional cubical complexes

2021 ◽  
Vol 9 ◽  
Author(s):  
Matthew Kahle ◽  
Elliot Paquette ◽  
Érika Roldán
Keyword(s):  
Fundamental Group ◽  
Random Graphs ◽  
High Probability ◽  
Cubical Complex ◽  
Sharp Threshold ◽  
Cubical Complexes ◽  
Simple Connectivity ◽  
Dimensional Cube ◽  
Dimensional Face ◽  
Connectivity Threshold

Abstract We study a natural model of a random $2$ -dimensional cubical complex which is a subcomplex of an n-dimensional cube, and where every possible square $2$ -face is included independently with probability p. Our main result exhibits a sharp threshold $p=1/2$ for homology vanishing as $n \to \infty $ . This is a $2$ -dimensional analogue of the Burtin and Erdoős–Spencer theorems characterising the connectivity threshold for random graphs on the $1$ -skeleton of the n-dimensional cube. Our main result can also be seen as a cubical counterpart to the Linial–Meshulam theorem for random $2$ -dimensional simplicial complexes. However, the models exhibit strikingly different behaviours. We show that if $p> 1 - \sqrt {1/2} \approx 0.2929$ , then with high probability the fundamental group is a free group with one generator for every maximal $1$ -dimensional face. As a corollary, homology vanishing and simple connectivity have the same threshold, even in the strong ‘hitting time’ sense. This is in contrast with the simplicial case, where the thresholds are far apart. The proof depends on an iterative algorithm for contracting cycles – we show that with high probability, the algorithm rapidly and dramatically simplifies the fundamental group, converging after only a few steps.

scholarly journals On the asymptotic topology of groups and spaces. Part II

2014 ◽  
Vol 55 ◽  
Author(s):  
Daniele Ettore Otera
Keyword(s):  
Simple Connectivity ◽  
Recent Developments

This note continues the study of the topology at infinity of groups and manifolds. Here we will quickly review the notion of geometric simple connectivity together with some more recent developments of it for groups.

scholarly journals Commensurated subgroups, semistability and simple connectivity at infinity

2014 ◽  
Vol 14 (6) ◽  
pp. 3509-3532 ◽  
Author(s):  
Gregory R Conner ◽  
Michael L Mihalik
Keyword(s):  
Simple Connectivity

scholarly journals A refinement of the simple connectivity at infinity for groups

2003 ◽  
Vol 81 (3) ◽  
pp. 360-368 ◽  
Author(s):  
L. Funar ◽  
D. E. Otera
Keyword(s):  
Simple Connectivity

scholarly journals Simple Connectivity of the Quillen Complex of GLn(q)

1995 ◽  
Vol 178 (1) ◽  
pp. 239-263 ◽  
Author(s):  
K.M. Das
Keyword(s):  
Simple Connectivity

Spatial Distribution and Fractal Properties of Aggregating Magnetic and Non-Magnetic Particles

Fractals ◽  
1998 ◽  
Vol 06 (03) ◽  
pp. 219-230 ◽  
Author(s):  
A. Provata ◽  
K. N. Trohidou
Keyword(s):  
Spatial Distribution ◽  
Fractal Dimension ◽  
Magnetic Particles ◽  
Composite System ◽  
System Size ◽  
Real Space ◽  
Magnetic Clusters ◽  
Self Similarity ◽  
Fractal Properties ◽  
Simple Connectivity

We study the spatial distribution in aggregating systems of mixtures of magnetic and non-magnetic particles using Monte-Carlo simulations together with scaling arguments. In particular, we show that (a) as the system size grows, the fractal dimension of the composite system is dominated by the smaller fractal dimension, (b) the system is realized as a back-bone consisting of magnetic particles (lower fractal dimension) with denser regions of non-magnetic particles attached to it at random positions. Using simple connectivity features observed in pure magnetic and non-magnetic clusters and self-similarity arguments we predict, via Real-Space-Renormalization, fractal exponents Dm = 1.25 ± 0.05 for the magnetic clusters and Dnm = 1.4 ± 0.1 for the non-magnetic clusters.

SIMPLE CONNECTIVITY MEASURES IN SPATIAL ECOLOGY

Ecology ◽  
2002 ◽  
Vol 83 (4) ◽  
pp. 1131-1145 ◽  
Author(s):  
Atte Moilanen ◽  
Marko Nieminen
Keyword(s):  
Spatial Ecology ◽  
Simple Connectivity

ON THE POSET OF NON-TRIVIAL PROPER SUBGROUPS OF A FINITE GROUP

2003 ◽  
Vol 02 (02) ◽  
pp. 165-168 ◽  
Author(s):  
MARIA SILVIA LUCIDO
Keyword(s):  
Finite Group ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Connected Components ◽  
Partially Ordered ◽  
Simple Connectivity ◽  
A Finite Group

In this paper we describe the connected components of ℒ(G), the partially ordered set of non-trivial proper subgroups of a finite group G. This result is related to the study of the simple connectivity of the coset poset of a finite group.

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