# Torus actions on oriented manifolds of generalized odd type

## TL;DR

This paper extends a known vanishing result of the signature for spin manifolds with odd type circle actions to more general torus actions on oriented manifolds of generalized odd type.

## Contribution

It generalizes the vanishing theorem from circle actions on spin manifolds to torus actions on oriented manifolds with a broader odd type condition.

## Key findings

- Signature vanishes for torus actions of generalized odd type
- Extends Landweber and Stong's result to higher-dimensional torus actions
- Provides new conditions under which the signature must be zero

## Abstract

Landweber and Stong prove that if a closed spin manifold $M$ admits a smooth $S^1$-action of odd type, then its signature $\mathrm{sign}(M)$ vanishes. In this paper, we extend the result to a torus action on a closed oriented manifold with generalized odd type.