On a generalized conjecture of Hopf with symmetry

A famous conjecture of Hopf is that the product of the two-dimensional sphere with itself does not admit a Riemannian metric with positive sectional curvature. More generally, one may conjecture that this holds for any nontrivial product. We provide evidence for this generalized conjecture in the presence of symmetry.Comment: 10 page

Positive curvature and rational ellipticity

Simply-connected manifolds of positive sectional curvature $M$ are speculated to have a rigid topological structure. In particular, they are conjectured to be rationally elliptic, i.e., all but finitely many homotopy groups are conjectured to be finite. In this article we combine positive curvature with rational ellipticity to obtain several topological properties of the underlying manifold. These results include a small upper bound on the Euler characteristic and confirmations of famous conjectures by Hopf and Halperin under additional torus symmetry. We prove several cases (including all known even-dimensional examples of positively curved manifolds) of a conjecture by Wilhelm

Diplopia and eye movement disorders.

Published versio

Skill and Australia's productivity surge

Skill and Australia’s Productivity Surge examines the changing demand for skills and the effect of increased skill on productivity growth. It finds that Australia’s productivity surge post 1993-94 was mainly due to factors other than the increase in the skill of the workforce.skill - productivity - labour - MFP - employment

How to Raise the Chicks

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