Higher \A-genera on certain non-spin $S^1$-manifolds

TL;DR

This paper proves that certain higher A-hat-genera vanish on smooth manifolds with effective circle actions, especially those with finite second and fourth homotopy groups, advancing understanding in equivariant topology.

Contribution

It establishes the vanishing of higher A-hat-genera on specific non-spin S^1-manifolds with finite homotopy groups, extending previous results in equivariant index theory.

Findings

Higher A-hat-genera vanish on these manifolds.

Vanishing applies to manifolds with finite second and fourth homotopy groups.

Results contribute to the understanding of equivariant index theory.

Abstract

We prove the vanishing of higher A-hat-genera, in the sense of Browder and Hsiang, on smooth manifolds with effective circle actions and with finite second and fourth homotopy groups