The isomorphism conjecture for Artin groups

TL;DR

This paper proves the Farrell-Jones fibered isomorphism conjecture for certain Artin groups, enabling explicit computation of their surgery obstruction groups, advancing understanding in algebraic K-theory and geometric topology.

Contribution

It establishes the conjecture for classes of Artin groups of finite and affine types, providing new results in algebraic topology.

Findings

Proved the Farrell-Jones conjecture for specific Artin groups

Computed surgery obstruction groups for finite type pure Artin groups

Enhanced understanding of algebraic K-theory for these groups

Abstract

We prove the Farrell-Jones fibered isomorphism conjecture for several classes of Artin groups of finite and affine types. As a consequence, we compute explicitly the surgery obstruction groups of the finite type pure Artin groups.