The $K$ and $L$ theoretic Farrell-Jones isomorphism conjecture for braid groups

TL;DR

This paper proves the $K$ and $L$ theoretic Farrell-Jones isomorphism conjecture for braid groups on surfaces, advancing understanding of algebraic K- and L-theory in geometric group theory.

Contribution

It establishes the conjecture for a new class of groups, specifically braid groups on surfaces, which was previously unresolved.

Findings

Proves the $K$-theoretic Farrell-Jones conjecture for braid groups on surfaces.

Proves the $L$-theoretic Farrell-Jones conjecture for braid groups on surfaces.

Extends the class of groups for which the Farrell-Jones conjecture is known to hold.

Abstract

We prove the $K$ and $L$ theoretic versions of the Fibered Isomorphism Conjecture of F. T. Farrell and L. E. Jones for braid groups on a surface.