Torus Actions, Fixed-Point Formulas, Elliptic Genera and positive curvature

TL;DR

This paper explores the fixed points of smooth torus actions on closed manifolds, utilizing fixed point formulas and equivariant elliptic genera, with applications to positively curved Riemannian manifolds exhibiting symmetry.

Contribution

It introduces new methods for analyzing fixed points of torus actions and applies elliptic genera to positively curved manifolds with symmetry.

Findings

Derived fixed point formulas for torus actions

Connected elliptic genera with positive curvature properties

Provided new insights into symmetry in positively curved manifolds

Abstract

We study fixed points of smooth torus actions on closed manifolds using fixed point formulas and equivariant elliptic genera. We also give applications to positively curved Riemannian manifolds with symmetry.