We consider two natural embeddings between Artin groups: the group GÃn-1 of type Ãn-1 embeds into the group GBn of type Bn; GBn in turn embeds into the classical braid group Brn+1:=GAn of type An. The cohomologies of these groups are related, by standard results, in a precise way. By using techniques developed in previous papers, we give precise formulas (sketching the proofs) for the cohomology of GBn with coefficients over the module Q[q±1,t±1], where the action is (-q)–multiplication for the standard generators associated to the first n-1 nodes of the Dynkin diagram, while is (-t)–multiplication for the generator associated to the last node.
Cohomology of Artin groups of type ~A_n, B_n and applications
CALLEGARO, FILIPPO GIANLUCA;SALVETTI, MARIO;
2008-01-01
Abstract
We consider two natural embeddings between Artin groups: the group GÃn-1 of type Ãn-1 embeds into the group GBn of type Bn; GBn in turn embeds into the classical braid group Brn+1:=GAn of type An. The cohomologies of these groups are related, by standard results, in a precise way. By using techniques developed in previous papers, we give precise formulas (sketching the proofs) for the cohomology of GBn with coefficients over the module Q[q±1,t±1], where the action is (-q)–multiplication for the standard generators associated to the first n-1 nodes of the Dynkin diagram, while is (-t)–multiplication for the generator associated to the last node.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
