ABELIAN AND METABELIAN QUOTIENT GROUPS OF SURFACE BRAID GROUPS

2016 ◽  
Vol 59 (1) ◽  
pp. 119-142 ◽  
Author(s):  
PAOLO BELLINGERI ◽  
EDDY GODELLE ◽  
JOHN GUASCHI
Keyword(s):  
Braid Groups ◽  
Rigidity Results ◽  
Group Presentations ◽  
Quotient Groups ◽  
Exact Sequences

AbstractIn this paper, we study Abelian and metabelian quotients of braid groups of oriented surfaces with boundary components. We provide group presentations and we prove rigidity results for these quotients arising from exact sequences related to (generalised) Fadell–Neuwirth fibrations.

POSITIVE PRESENTATIONS OF SURFACE BRAID GROUPS

2007 ◽  
Vol 16 (09) ◽  
pp. 1219-1233 ◽  
Author(s):  
PAOLO BELLINGERI ◽  
EDDY GODELLE
Keyword(s):  
Conjugacy Problem ◽  
Braid Groups ◽  
Group Presentations ◽  
Positive Presentations

We provide new group presentations for surface braid groups which are positive. We study some properties of such presentations and we solve the conjugacy problem in a particular case.

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

The category of exact sequences of Banach spaces

2010 ◽  
pp. 139-158 ◽  
Author(s):  
Jesús M. F. Castillo ◽  
Yolanda Moreno
Keyword(s):  
Banach Spaces ◽  
Exact Sequences

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

scholarly journals Path homology theory of edge-colored graphs

2021 ◽  
Vol 19 (1) ◽  
pp. 706-723
Author(s):  
Yuri V. Muranov ◽  
Anna Szczepkowska
Keyword(s):  
Spectral Sequence ◽  
Edge Coloring ◽  
Homology Theory ◽  
Homotopy Category ◽  
Homology Groups ◽  
Colored Graphs ◽  
Natural Filtration ◽  
Definition Of ◽  
Exact Sequences

Abstract In this paper, we introduce the category and the homotopy category of edge-colored digraphs and construct the functorial homology theory on the foundation of the path homology theory provided by Grigoryan, Muranov, and Shing-Tung Yau. We give the construction of the path homology theory for edge-colored graphs that follows immediately from the consideration of natural functor from the category of graphs to the subcategory of symmetrical digraphs. We describe the natural filtration of path homology groups of any digraph equipped with edge coloring, provide the definition of the corresponding spectral sequence, and obtain commutative diagrams and braids of exact sequences.

scholarly journals The $$R_\infty $$ property for pure Artin braid groups

2021 ◽  
Vol 195 (1) ◽  
pp. 15-33
Author(s):  
Karel Dekimpe ◽  
Daciberg Lima Gonçalves ◽  
Oscar Ocampo
Keyword(s):  
Braid Groups
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