An appendix to a paper by B. Hanke and T. Schick

TL;DR

This paper offers a concise, unified proof that low-dimensional higher A-genera vanish for spin manifolds with positive scalar curvature, avoiding reliance on the strong Novikov conjecture.

Contribution

It provides a new, simplified proof of a known result on the vanishing of higher A-genera for certain spin manifolds, extending previous methods.

Findings

Proves vanishing of low-dimensional higher A-genera for spin manifolds with positive scalar curvature

Avoids using the strong Novikov conjecture in the proof

Provides a unified and concise proof approach

Abstract

In this short note we apply methods introduced by B. Hanke and T. Shick to prove the vanishing of (low dimensional) higher $A$-genera for spin manifolds admitting a positive scalar curvature metric. Our aim is to provide a short and unified proof for this beautiful result without using the strong Novikov conjecture.