Anand Dessai

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math.DG2001

Obstructions to positive curvature and symmetry

Anand Dessai

We show that the indices of certain twisted Dirac operators vanish on a $S p in$ -manifold $M$ of positive sectional curvature if the symmetry rank of $M$ is $\geq 2$ or if the symmet…

math.DG2000

On the topology of scalar-flat manifolds

Anand Dessai

Let $M$ be a simply-connected closed manifold of dimension $\geq 5$ which does not admit a metric with positive scalar curvature. We give necessary conditions for $M$ to admit a sc…