Doubled α ′-geometry

Doubled Geometry and T-Folds

The doubled formulation of string theory, which is T-duality covariant and enlarges spacetime with extra coordinates conjugate to winding number, is reformulated and its geometric and topological features examined. It is used to formulate string theory in T-fold backgrounds with T-duality transition functions and a quantum implementation of the constraints of the doubled formalism is presented....

F-Geometry and Amari's α-Geometry on a Statistical Manifold

Optimal carbon tax doubled

Typically, cost–benefit analysis (CBA) has suggested ‘optimal’ carbon tax regimes that result in a global temperature rise of around 3 °C, or even eventually (post-2100) 4 °C, above preindustrial levels. However, risk analysis approaches indicate that these levels of temperature rise result in climate change impacts that pose a high or very high level of risk to society and ecosystems1 (Fig. 1)...

On the doubled tetrus

This paper describes some properties of a certain fibered hyperbolic 3manifold which arises ”in nature”; that is, as the cover of a closed manifold constructed by other means. Among other things, the main theorem answers in the affirmative the question of whether it is possible for a fibered hyperbolic manifold to be a double across a connected surface. (We first heard this question from Alan R...

Doubled quadratic division algebras

The concept of doubling, introduced around 1840 by Hamilton and Graves, associates with any quadratic algebra A over a field k of characterstic not 2 its double V(A) = A×A, with multiplication (w, x)(y, z) = (wy− z̄x, xȳ + zw). It yields an endofunctor on the category of all quadratic k-algebras which is faithful but not full. We study in which respect the division property of a quadratic k-alge...