Covers of D-Type Artin Groups
نویسندگان
چکیده
We study certain quotients of generalized Artin groups which have a natural map onto D-type Artin groups, where the generalized Artin group A(T ) is defined by a signed graph T . Then we find a certain quotient G(T ) according to the graph T , which also have a natural map onto A(Dn). We prove that G(T ) is isomorphic to a semidirect product of a group K(m,n), with the Artin group A(Dn), where K (m,n) depends only on the number m of cycles and on the number n of vertices of the graph T .
منابع مشابه
Artin Covers of the Braid Groups
Computation of fundamental groups of Galois covers recently led to the construction and analysis of Coxeter covers of the symmetric groups [RTV]. In this paper we consider analog covers of Artin’s braid groups, and completely describe the induced geometric extensions of the braid group.
متن کاملBestvina’s Normal Form Complex and the Homology of Garside Groups
A Garside group is a group admitting a finite lattice generating set D. Using techniques developed by Bestvina for Artin groups of finite type, we construct K(π, 1)s for Garside groups. This construction shows that the (co)homology of any Garside group G is easily computed given the lattice D, and there is a simple sufficient condition that implies G is a duality group. The universal covers of ...
متن کاملA Combination Theorem for Special Cube Complexes
We prove that certain compact cube complexes have special finite covers. This means they have finite covers whose fundamental groups are quasiconvex subgroups of right-angled Artin groups. As a result we obtain, linearity and the separability of quasiconvex subgroups, for the groups we consider. Our result applies in particular to compact negatively curved cube complexes whose hyperplanes don’t...
متن کاملA combination theorem for special cube complexes
We prove that certain compact cube complexes have special finite covers. This means they have finite covers whose fundamental groups are quasiconvex subgroups of right-angled Artin groups. As a result we obtain linearity and the separability of quasiconvex subgroups for the groups we consider. Our result applies, in particular, to a compact negatively curved cube complex whose hyperplanes do no...
متن کاملLocal indicability and commutator subgroups of Artin groups
Artin groups (also known as Artin-Tits groups) are generalizations of Artin’s braid groups. This paper concerns Artin groups of spherical type, that is, those whose corresponding Coxeter group is finite, as is the case for the braid groups. We compute presentations for the commutator subgroups of the irreducible spherical-type Artin groups, generalizing the work of Gorin and Lin [GL69] on the b...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 24 شماره
صفحات -
تاریخ انتشار 2017