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A certain structure of Artin groups and the isomorphism conjecture

S. K. Roushon

Abstract

We observe an inductive structure in a large class of Artin groups and exploit this information to deduce the Farrell-Jones isomorphism conjecture for several classes of Artin groups of finite real, complex and affine types.

A certain structure of Artin groups and the isomorphism conjecture

Abstract

We observe an inductive structure in a large class of Artin groups and exploit this information to deduce the Farrell-Jones isomorphism conjecture for several classes of Artin groups of finite real, complex and affine types.

Paper Structure

This paper contains 6 sections, 14 theorems, 18 equations.

Table of Contents

  1. Introduction
  2. Artin groups
  3. Statements of results
  4. Artin groups and orbifold braid groups
  5. Proofs of Theorems \ref{['orbi-poly-free']} and \ref{['d-b']}
  6. Computation of the surgery groups

Key Result

Theorem 1.1

Let $\Gamma$ be an Artin group of type $A_n$, $B_n (=C_n)$, $D_n$, $F_4$, $G_2$, $I_2(p)$, $\tilde{A}_n$, $\tilde{B}_n$, $\tilde{C}_n$ or $G(de,e,r)$ ($d,r\geq 2$). Then the isomorphism conjecture in $K$-, $L$- and $A$-theories with coefficients and finite wreath product is true for any subgroup of

Theorems & Definitions (33)

  • Theorem 1.1
  • proof
  • Corollary 1.1
  • Remark 2.1
  • Definition 2.1
  • Theorem 2.1
  • Definition 3.1
  • Theorem 3.1
  • Theorem 3.2
  • Theorem 3.3
  • ...and 23 more