Composition algebras and the two faces of G2G_{2}

We consider composition and division algebras over the real numbers: We note two r\^oles for the group $G_{2}$: as automorphism group of the octonions and as the isotropy group of a generic 3-form in 7 dimensions. We show why they are equivalent, by means of a regular metric. We express in some diagrams the relation between some pertinent groups, most of them related to the octonions. Some applications to physics are also discussed.Comment: 11 pages, 3 figure

Moduli spaces of G2 manifolds

This paper is a review of current developments in the study of moduli spaces of G2 manifolds. G2 manifolds are 7-dimensional manifolds with the exceptional holonomy group G2. Although they are odd-dimensional, in many ways they can be considered as an analogue of Calabi-Yau manifolds in 7 dimensions. They play an important role in physics as natural candidates for supersymmetric vacuum solutions of M-theory compactifications. Despite the physical motivation, many of the results are of purely mathematical interest. Here we cover the basics of G2 manifolds, local deformation theory of G2 structures and the local geometry of the moduli spaces of G2 structures.Comment: 31 pages, 2 figure

The G_2 sphere over a 4-manifold

We present a construction of a canonical G_2 structure on the unit sphere tangent bundle S_M of any given orientable Riemannian 4-manifold M. Such structure is never geometric or 1-flat, but seems full of other possibilities. We start by the study of the most basic properties of our construction. The structure is co-calibrated if, and only if, M is an Einstein manifold. The fibres are always associative. In fact, the associated 3-form results from a linear combination of three other volume 3-forms, one of which is the volume of the fibres. We also give new examples of co-calibrated structures on well known spaces. We hope this contributes both to the knowledge of special geometries and to the study of 4-manifolds.Comment: 13 page

Active Amplification of the Terrestrial Albedo to Mitigate Climate Change: An Exploratory Study

This study explores the potential to enhance the reflectance of solar insolation by the human settlement and grassland components of the Earth's terrestrial surface as a climate change mitigation measure. Preliminary estimates derived using a static radiative transfer model indicate that such efforts could amplify the planetary albedo enough to offset the current global annual average level of radiative forcing caused by anthropogenic greenhouse gases by as much as 30 percent or 0.76 W/m2. Terrestrial albedo amplification may thus extend, by about 25 years, the time available to advance the development and use of low-emission energy conversion technologies which ultimately remain essential to mitigate long-term climate change. However, additional study is needed to confirm the estimates reported here and to assess the economic and environmental impacts of active land-surface albedo amplification as a climate change mitigation measure.Comment: 21 pages, 3 figures. In press with Mitigation and Adaptation Strategies for Global Change, Springer, N

Self-Duality in D <= 8-dimensional Euclidean Gravity

In the context of D-dimensional Euclidean gravity, we define the natural generalisation to D-dimensions of the self-dual Yang-Mills equations, as duality conditions on the curvature 2-form of a Riemannian manifold. Solutions to these self-duality equations are provided by manifolds of SU(2), SU(3), G_2 and Spin(7) holonomy. The equations in eight dimensions are a master set for those in lower dimensions. By considering gauge fields propagating on these self-dual manifolds and embedding the spin connection in the gauge connection, solutions to the D-dimensional equations for self-dual Yang-Mills fields are found. We show that the Yang-Mills action on such manifolds is topologically bounded from below, with the bound saturated precisely when the Yang-Mills field is self-dual. These results have a natural interpretation in supersymmetric string theory.Comment: 9 pages, Latex, factors in eqn. (6) corrected, acknowledgement and reference added, typos fixe