Polynomially bounded cohomology and the Novikov Conjecture

TL;DR

This paper proves that for all finitely presented discrete groups, the assembly map in polynomially bounded cohomology is rationally injective, supporting the $ ext{L}^1$-analogue of the Strong Novikov Conjecture.

Contribution

It establishes the rational injectivity of the assembly map in polynomially bounded cohomology for finitely presented groups, verifying the $ ext{L}^1$-analogue of the Strong Novikov Conjecture.

Findings

Rational injectivity of the assembly map for finitely presented groups.

Verification of the $ ext{L}^1$-analogue of the Strong Novikov Conjecture.

Application of polynomially bounded cohomology techniques.

Abstract

Using techniques developed for studying polynomially bounded cohomology, we show that the assembly map for $K_*^t(\ell^1(G))$ is rationally injective for all finitely presented discrete groups $G$. This verifies the $\ell^1$-analogue of the Strong Novikov Conjecture for such groups.