Artin Groups, 3-manifolds and Coherence
نویسندگان
چکیده
1. Introduction. By a labeled graph we shall mean a finite (non-empty) graph Γ, without loops or multiple edges, each of whose edges is labeled by an integer greater than or equal to 2. Let the vertices of Γ be s 1 , s 2 ,. .. , s n , and let the label on an edge with endpoints s i and s j be m ij ≥ 2. Define ab m to be the word abab. .. of length m. Then the Artin group AΓ associated with the labeled graph Γ is the group with generators s 1 , s 2 ,. .. , s n , and relations s i s j m ij = s j s i m ij , one for each edge of Γ. In particular, if m ij = 2 then the generators
منابع مشابه
Actions of right-angled Artin groups in low dimensions
We survey the role of right-angled Artin groups in the theory of diffeomorphism groups of low dimensional manifolds. We first describe some of the subgroup structure of right-angled Artin groups. We then discuss the interplay between algebraic structure, compactness, and regularity for group actions on one–dimensional manifolds. For compact one–manifolds, every right-angled Artin group acts fai...
متن کاملQuasi-isometric Classification of Graph Manifolds Groups
We show that the fundamental groups of any two closed irreducible non-geometric graph-manifolds are quasi-isometric. This answers a question of Kapovich and Leeb. We also classify the quasi-isometry types of fundamental groups of graph-manifolds with boundary in terms of certain finite two-colored graphs. A corollary is a quasi-isometry classification of Artin groups whose presentation graphs a...
متن کاملMarkov Theorems for Links in 3-manifolds
We describe here a Markov theorem for links in S 2 S 1 using the braid groups corresponding to the Coxeter groups of type B l. See the theorem in x3. We will work on a more general setting. The only reason here to single out S 2 S 1 is its simplicity. It is possible that all the other Artin groups will turn out to be useful in the study of links in 3-manifolds.
متن کاملOn Shephard groups with large triangles
Shephard groups are common extensions of Artin and Coxeter groups. They appear, for example, in algebraic study of manifolds. An infinite family of Shephard groups which are not Artin or Coxeter groups is considered. Using techniques form small cancellation theory we show that the groups in this family are bi-automatic.
متن کاملVirtual Cubulation of Nonpositively Curved Graph Manifolds
In this paper, we show that an aspherical compact graph manifold is nonpositively curved if and only if its fundamental group virtually embeds into a right-angled Artin group. As a consequence, nonpositively curved graph manifolds have linear fundamental groups.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003