Wilderich Tuschmann

Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces

We show that almost nonnegatively curved m-dimensional manifolds are, up to finite cover, nilpotent spaces in the sense of homotopy theory and have C(m)-nilpotent fundamental groups. We also show that up to a finite cover almost nonnegatively curved manifolds are fiber bundles with simply connected fibers over nilmanifolds.

Non-negative pinching, moduli spaces and bundles with infinitely many souls

We show that in each dimension

Asymptotical flatness and cone structure at infinity

n\ge 10

INVARIANT METRICS OF POSITIVE RICCI CURVATURE ON PRINCIPAL BUNDLES

there exist infinite sequences of homotopy equivalent but mutually non-homeomorphic closed simply connected Riemannian

Moduli Spaces of Riemannian Metrics

n

Dually Flat Manifolds and Global Information Geometry

-manifolds with

Collapsing, solvmanifolds and infrahomogeneous spaces

0\le \sec\le 1

Smooth diameter and eigenvalue rigidity in positive Ricci curvature

, positive Ricci curvature and uniformly bounded diameter. We also construct open manifolds of fixed diffeomorphism type which admit infinitely many complete nonnegatively pinched metrics with souls of bounded diameter such that the souls are mutually non-homeomorphic. Finally, we construct examples of noncompact manifolds whose moduli spaces of complete metrics with

Nonconnected moduli spaces of nonnegative sectional curvature metrics on simply connected manifolds

\sec\ge 0

Manifolds with almost nonnegative curvature operator and principal bundles

have infinitely many connected components.