Homomorphisms of commutator subgroups of braid groups

نویسندگان

چکیده

We give a complete classification of homomorphisms from the commutator subgroup braid group on n $n$ strands to when is at least 7. In particular, we show that each non-trivial homomorphism extends an automorphism strands. This answers four questions Vladimir Lin. Our main new tool theory totally symmetric sets.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Pure Braid Subgroups of Braided Thompson’s Groups

We describe pure braided versions of Thompson’s group F . These groups, BF and B̂F , are subgroups of the braided versions of Thompson’s group V , introduced by Brin and Dehornoy. Unlike V , elements of F are order-preserving self-maps of the interval and we use pure braids together with elements of F thus preserving order. We define these groups and give normal forms for elements and describe i...

متن کامل

Brunnian subgroups of mapping class groups and braid groups

In this paper we continue our study of the Delta-group structure on the braid groups and mapping class groups of a surface. We calculate the homotopy groups of these Delta-groups and prove some results about Brunnian braid groups and Brunnian mapping class groups. This is the second of a pair of papers on these structures.

متن کامل

Local 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 کامل

Quasi-isometrically Embedded Subgroups of Braid and Diffeomorphism Groups

We show that a large class of right-angled Artin groups (in particular, those with planar complementary defining graph) can be embedded quasi-isometrically in pure braid groups and in the group Diff(D2, ∂D2, vol) of area preserving diffeomorphisms of the disk fixing the boundary (with respect to the L2-norm metric); this extends results of Benaim and Gambaudo who gave quasi-isometric embeddings...

متن کامل

Representations of Braid Groups via Conjugation Actions on Congruence Subgroups

where α and β are nonzero complex numbers. If α, β lie in some subfield F of C, then the representations are defined over F (in fact, over Z[α±1, β±1]). The starting point for ρn(α) is the reduced Burau representation βn : Bn → GLn−1(Z[t, t −1]). For each i ≥ 1, set K(α) = {A ∈ SLn−1(C[t, t ]) : A ≡ I mod (t− α)}. The sequence {K(α)}i≥1 is a central series inK(α) = K 1(α) (i.e., Ki+j(α) ⊇ [K(α)...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Bulletin of The London Mathematical Society

سال: 2022

ISSN: ['1469-2120', '0024-6093']

DOI: https://doi.org/10.1112/blms.12560