H-Space structures on spaces of metrics of positive scalar curvature

We construct and study an $H$-space multiplication on $\mathcal R^+(M)$ for manifolds $M$ which are nullcobordant in their own tangential $2$-type. This is applied to give a rigidity criterion for the action of the diffeomorphism group on $\mathcal R^+(M)$ via pullback. We also compare this to other known multiplicative structures on $\mathcal R^+(M)$.Comment: 15 pages, 21 figures; v2: revision according to referee report, accepted for publication in Trans. Amer. Math. So

The Gromov–Lawson–Chernysh surgery theorem

This is an expository article without any claim of originality. We give a complete and self-contained account of the Gromov–Lawson–Chernysh surgery theorem for positive scalar curvature metrics

Spaces of positive intermediate curvature metrics

In this paper we study spaces of Riemannian metrics with lower bounds on intermediate curvatures. We show that the spaces of metrics of positive p-curvature and k-positive Ricci curvature on a given high-dimensional Spin-manifold have many non-trivial homotopy groups provided that the manifold admits such a metric.Comment: 34 page

Cohomogeneity one manifolds and homogeneous spaces of positive scalar curvature

We characterize cohomogeneity one manifolds and homogeneous spaces with a compact Lie group action admitting an invariant metric with positive scalar curvature

Concurrent elevation of CO₂, O₃ and temperature severely affects oil quality and quantity in rapeseed

Plant oil is an essential dietary and bio-energy resource. Despite this, the effects of climate change on plant oil quality remain to be elucidated. The present study is the first to show changes in oil quality and quantity of four rapeseed cultivars in climate scenarios with elevated [CO(2)], [O(3)] and temperature (T) combined and as single factors. The combination of environmental factors resembled IPCC’s ‘business as usual’ emission scenario predicted for late this century. Generally, the climate scenarios reduced the average amounts of the six fatty acids (FAs) analysed, though in some treatments single FAs remained unchanged or even increased. Most reduced was the FA essential for human nutrition, C18:3-ω3, which decreased by 39% and 45% in the combined scenarios with elevated [CO(2)]+T+[O(3)] and [CO(2)]+T, respectively. Average oil content decreased 3–17%. When [CO(2)] and T were elevated concurrently, the seed biomass was reduced by half, doubling the losses in FAs and oil content. This corresponded to a 58% reduction in the oil yield per hectare, and C18:3-ω3 decreased by 77%. Furthermore, the polyunsaturated FAs were significantly decreased. The results indicate undesirable consequences for production and health benefits of rapeseed oil with future climate change. The results also showed strong interactive effects of CO(2), T and O(3) on oil quality, demonstrating why prediction of climate effects requires experiments with combined factors and should not be based on extrapolation from single factor experiments