Positive curvature and the elliptic genus

Abstract

We prove several results about the vanishing of the elliptic genus on positively curved Spin manifolds with logarithmic symmetry rank. The proofs are based on the rigidity of the elliptic genus and Kennard's improvement of the Connectedness Lemma for transversely intersecting, totally geodesic submanifolds.

15 pages. Paper was rewritten. To appear in New York Journal of Mathematics

References in corpus (1)

• Topological properties of positively curved manifolds with symmetry

Cited by in corpus (1)

• Fundamental groups of manifolds with positive sectional curvature and torus symmetry