scholarly journals Fibered commensurability and arithmeticity of random mapping tori

2017 ◽  
Vol 11 (4) ◽  
pp. 1253-1279
Author(s):  
Hidetoshi Masai
Keyword(s):  
2019 ◽  
Vol 26 (1) ◽  
pp. 293-321 ◽  
Author(s):  
Alessandro Sisto ◽  
Samuel J. Taylor

1991 ◽  
Vol 23 (3) ◽  
pp. 437-455 ◽  
Author(s):  
P. J. Donnelly ◽  
W. J. Ewens ◽  
S. Padmadisastra

A random mapping partitions the set {1, 2, ···, m} into components, where i and j are in the same component if some functional iterate of i equals some functional iterate of j. We consider various functionals of these partitions and of samples from it, including the number of components of ‘small' size and of size O(m) as m → ∞the size of the largest component, the number of components, and various symmetric functionals of the normalized component sizes. In many cases exact results, while available, are uniformative, and we consider various approximations. Numerical and simulation results are also presented. A central tool for many calculations is the ‘frequency spectrum', both exact and asymptotic.


2021 ◽  
Vol 10 (2) ◽  
pp. 21
Author(s):  
Giovanni Montesano ◽  
Luca M. Rossetti ◽  
Davide Allegrini ◽  
Mario R. Romano ◽  
David F. Garway-Heath ◽  
...  

2018 ◽  
Vol 10 (5) ◽  
pp. 827-847 ◽  
Author(s):  
Cheng Li ◽  
Chenwei Deng ◽  
Shichao Zhou ◽  
Baojun Zhao ◽  
Guang-Bin Huang

2019 ◽  
Vol 2019 (748) ◽  
pp. 153-172 ◽  
Author(s):  
Ian Biringer ◽  
Juan Souto

Abstract We show that if ϕ is a homeomorphism of a closed, orientable surface of genus g, and ϕ has large translation distance in the curve complex, then the fundamental group of the mapping torus {M_{\phi}} has rank {2g+1} .


2013 ◽  
Vol 50 (3) ◽  
pp. 721-740 ◽  
Author(s):  
Jennie C. Hansen ◽  
Jerzy Jaworski

In this paper we characterise the distributions of the number of predecessors and of the number of successors of a given set of vertices, A, in the random mapping model, TnD̂ (see Hansen and Jaworski (2008)), with exchangeable in-degree sequence (D̂1,D̂2,…,D̂n). We show that the exact formulae for these distributions and their expected values can be given in terms of the distributions of simple functions of the in-degree variables D̂1,D̂2,…,D̂n. As an application of these results, we consider two special examples of TnD̂ which correspond to random mappings with preferential and anti-preferential attachment, and determine the exact distributions for the number of predecessors and the number of successors in these cases. We also characterise, for these two special examples, the asymptotic behaviour of the expected numbers of predecessors and successors and interpret these results in terms of the threshold behaviour of epidemic processes on random mapping graphs. The families of discrete distributions obtained in this paper are also of independent interest.


2019 ◽  
Vol 31 (4) ◽  
pp. 907-915 ◽  
Author(s):  
Giovanni Bazzoni ◽  
Oliver Goertsches

Abstract We show that compact toric cosymplectic manifolds are mapping tori of equivariant symplectomorphisms of toric symplectic manifolds.


1997 ◽  
Vol 06 (06) ◽  
pp. 827-831 ◽  
Author(s):  
Takayuki Morifuji

We give a characterization for the reducibility of elements of any finite subgroup of the mapping class group of genus 2 surface in terms of the η-invariant of finite order mapping tori.


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