A stability-like theorem for cohomology of pure braid groups of the series A, B and D
| dc.creator | Settepanella, Simona | |
| dc.date | 2003-07-10 | |
| dc.date | 2003-10-15 | |
| dc.date.accessioned | 2026-07-07T04:59:35Z | |
| dc.date.available | 2026-07-07T04:59:35Z | |
| dc.description | Consider the ring $R:=\Q[τ,τ^{-1}]$ of Laurent polynomials in the variable $τ$. The Artin's Pure Braid Groups (or Generalized Pure Braid Groups) act over $R,$ where the action of every standard generator is the multiplication by $τ$. In this paper we consider the cohomology of such groups with coefficients in the module $R$ (it is well known that such cohomology is strictly related to the untwisted integral cohomology of the Milnor fibration naturally associated to the reflection arrangement). We give a sort of \textit{stability} theorem for the cohomologies of the infinite series $A$, $B$ and $D,$ finding that these cohomologies stabilize, with respect to the natural inclusion, at some number of copies of the trivial $R$-module $\Q$. We also give a formula which compute this number of copies. | |
| dc.description | 17 pages; added reference for section 1 | |
| dc.identifier | https://arxiv.org/abs/math/0307149 | |
| dc.identifier | http://arxiv.org/abs/math/0307149 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68045 | |
| dc.subject | Group Theory | |
| dc.subject | Category Theory | |
| dc.subject | 20J06 (20F36) | |
| dc.title | A stability-like theorem for cohomology of pure braid groups of the series A, B and D | |
| dc.type | text |