Tits alternative for Artin groups of type FC
نویسندگان
چکیده
منابع مشابه
Multifraction reduction I: The 3-Ore case and Artin-Tits groups of type FC
We describe a new approach to the word problem for Artin-Tits groups and, more generally, for the enveloping group U(M) of a monoid M in which any two elements admit a greatest common divisor. The method relies on a rewrite system RM that extends free reduction for free groups. Here we show that, if M satisfies what we call the 3-Ore condition about common multiples, what corresponds to type FC...
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This paper is a short survey on four basic questions on Artin-Tits groups: the torsion, the center, the word problem, and the cohomology (K(π, 1) problem). It is also an opportunity to prove three new results concerning these questions: (1) if all free of infinity Artin-Tits groups are torsion free, then all Artin-Tits groups will be torsion free; (2) If all free of infinity irreducible non-sph...
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The group AS is called an Artin group and relations sts . . . } {{ } ms,t terms = tst . . . } {{ } ms,t terms are called braid relations. For instance, if S = {s1, . . . , sn} with msi,sj = 3 for |i − j| = 1 and msi,sj = 2 otherwise, then the associated Artin group is the braid group. We denote by A+S the submonoid of AS generated by S. This monoid A+S has the same presentation as the group AS ...
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We conjecture that the word problem of Artin–Tits groups can be solved without introducing trivial factors ss or ss. Here we make this statement precise and explain how it can be seen as a weak form of hyperbolicity. We prove the conjecture in the case of Artin–Tits groups of type FC, and we discuss various possible approaches for further extensions, in particular a syntactic argument that work...
متن کاملLecture Notes on Artin–tits Groups
1 0.1. Braid groups 1 0.2. Artin–Tits groups 2 1. The general case 2 1.1. The word reversing technique 3 1.2. Artin–Tits monoids 4 1.3. Artin–Tits groups 5 1.4. Exercises 5 2. The spherical case 6 2.1. Background about Coxeter groups 6 2.2. Garside structure 7 2.3. Normal form 7 2.4. Exercises 8 3. The braid case 9 3.1. The Artin representation 10 3.2. Handle reduction 11 3.3. The braid orderin...
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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2020
ISSN: 1435-4446,1433-5883
DOI: 10.1515/jgth-2019-0135