Injective maps between Artin groups


John Crisp


Research Report 97-10
Date: 27 March 1997


A sufficient condition is given for the injectivity of a homomorphism between Artin monoids which moreover ensures injectivity of the induced map between Artin groups in the case where both groups are of finite type. We list numerous examples of monoid homomorphisms satisfying this injectivity condition, all of which happen to be so-called LCM-homomorphisms.

In the case of an LCM-homomorphism there is a natural way to realise the corresponding map on Artin groups geometrically as the map induced on fundamental groups by an inclusion of certain finite simplicial complexes.

An interesting group homomorphism which is not realised in this way exhibits the Artin group of type B_n as a subgroup of finite index of the classical (n+1)-string braid group (type A_n). This subgroup is in fact the group of n-string braids over an annulus.

Key phrases

Artin group. braid group. monoid. Salvetti complex.

AMS Subject Classification (1991)

Primary: 20F36


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