On Representations of Artin Groups and the Tits Conjecture
نویسندگان
چکیده
منابع مشابه
A conjecture about Artin-Tits groups
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...
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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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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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The Tits conjecture claims that the subgroup generated by the squares of the standard generators of an Artin group can be presented using only the obvious relations. We show that the Tits conjecture is true for the Artin groups of type Bn.
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The purpose of this paper is to put together a large amount of results on the K(π, 1) conjecture for Artin groups, and to make them accessible to non-experts. Firstly, this is a survey, containing basic definitions, the main results, examples and an historical overview of the subject. But, it is also a reference text on the topic that contains proofs of a large part of the results on this quest...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1994
ISSN: 0021-8693
DOI: 10.1006/jabr.1994.1312