Profinite Braid Groups, Galois Representations and Complex Multiplications

1986 ◽  
Vol 123 (1) ◽  
pp. 43 ◽  
Author(s):  
Yasutaka Ihara
Keyword(s):  
Galois Representations ◽  
Braid Groups ◽  
Complex Multiplications

Pseudo-Anosov Theory

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Braid Groups ◽  
Intersection Numbers ◽  
Branched Covers ◽  
Algebraic Integers ◽  
Dehn Twists ◽  
Mapping Classes ◽  
Dynamical Properties

This chapter focuses on the construction as well as the algebraic and dynamical properties of pseudo-Anosov homeomorphisms. It first presents five different constructions of pseudo-Anosov mapping classes: branched covers, constructions via Dehn twists, homological criterion, Kra's construction, and a construction for braid groups. It then proves a few fundamental facts concerning stretch factors of pseudo-Anosov homeomorphisms, focusing on the theorem that pseudo-Anosov stretch factors are algebraic integers. It also considers the spectrum of pseudo-Anosov stretch factors, along with the special properties of those measured foliations that are the stable (or unstable) foliations of some pseudo-Anosov homeomorphism. Finally, it describes the orbits of a pseudo-Anosov homeomorphism as well as lengths of curves and intersection numbers under iteration.

New Signature Scheme over the Braid Groups

2011 ◽  
Vol 32 (12) ◽  
pp. 2930-2934
Author(s):  
Yun Wei ◽  
Guo-hua Xiong ◽  
Wan-su Bao ◽  
Xing-kai Zhang
Keyword(s):  
Braid Groups ◽  
Signature Scheme

scholarly journals Crystallographic groups and flat manifolds from surface braid groups

2020 ◽  
pp. 107560
Author(s):  
Daciberg Lima Gonçalves ◽  
John Guaschi ◽  
Oscar Ocampo ◽  
Carolina de Miranda e Pereiro
Keyword(s):  
Braid Groups ◽  
Crystallographic Groups ◽  
Flat Manifolds
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