Related papers: A Remark on Coclosed G_2-Structures

We study nearly parallel $\mathrm{G}_{2}$-structures with a three-torus symmetry via multi-moment map techniques. An effective three-torus action on a nearly parallel $\mathrm{G}_{2}$-manifold yields a multi-moment map. The torus acts…

We describe the second order obstruction to deformation for nearly $G_2$ structures on compact manifolds. Building on work of B.Alexandrov and U.Semmelmann this allows proving rigidity under deformation for the proper nearly $G_2$ structure…

A torsion-free G_2 structure admitting an infinitesimal isometry is shown to give rise to a 4-manifold equipped with a complex symplectic structure and a 1-parameter family of functions and 2-forms linked by second order equations.…

In this short note we give an elementary proof of the fact that connections and their geometric parallel-transport counterpart are equivalent notions.

Given two homogeneous spaces of the form G_1/K and G_2/K, where G_1 and G_2 are compact simple Lie groups, we study the existence problem for G_1xG_2-invariant Einstein metrics on the homogeneous space M=G_1xG_2/K. For the large subclass C…

We consider higher dimensional generalisations of normal almost contact structures, the so called f.pk-structures where parallelism spans a Lie algebra g (f.pk-g-structures). Two types of these structures are discussed. In the first case,…

We show that C^2 conformally compact Riemannian Einstein metrics have conformal compactifications that are smooth up to the boundary in dimension 3 and all even dimensions, and polyhomogeneous in odd dimensions greater than 3.

We introduce the concept of generalized almost plastic structure, and, on a pseudo-Riemannian manifold endowed with two $(1,1)$-tensor fields satisfying some compatibility conditions, we construct a family of generalized almost plastic…

We study $GL(2)$-structures on differential manifolds. The structures play a fundamental role in the geometric theory of ordinary differential equations. We prove that any $GL(2)$-structure on an even dimensional manifold give rise to a…

We prove a rigidity theorem that shows that, under many circumstances, quasi-isometric embeddings of equal rank, higher rank symmetric spaces are close to isometric embeddings. We also produce some surprising examples of quasi-isometric…

We introduce a method to construct $G_2$-instantons over compact $G_2$-manifolds arising as the twisted connected sum of a matching pair of building blocks [Kov03,KL11,CHNP12]. Our construction is based on gluing $G_2$-instantons obtained…

We construct a Gelfand-Zeitlin system on a one-parameter family of $G_2$ coadjoint orbits that are multiplicity-free Hamiltonian $SU(3)$-spaces. Using this system we prove a lower bound for the Gromov width of these orbits. This lower bound…

We characterize the structure of a seven-dimensional Lie algebra with non-trivial center endowed with a closed G$_2$-structure. Using this result, we classify all unimodular Lie algebras with non-trivial center admitting closed…

The main results in this note concern the characterization of the length of continua 1 (Theorems 2.5) and the parametrization of continua with finite length (Theorem 4.4). Using these results we give two independent and relatively…

Over a field of characteristic zero, we show that two commutative differential graded (dg) algebras are quasi-isomorphic if and only if they are quasi-isomorphic as associative dg algebras. This answers a folklore problem in rational…

We prove isoperimetric inequalities for quotients of $n$-dimensional Affine buildings. We use these inequalities to prove topological overlapping for the 2-dimensional skeletons of these buildings.

It was first shown in (Catanese-LeBrun 1997) that certain high-dimensional smooth closed manifolds admit pairs of Einstein metrics with Ricci curvatures of opposite sign. After reviewing subsequent progress that has been made on this topic,…

In this article we study the stability problem for the Einstein metrics on Sasaki Einstein and on complete nearly parallel ${\rm G}_2$ manifolds. In the Sasaki case we show linear instability if the second Betti number is positive.…

In this note we prove three rigidity results for Einstein manifolds with bounded covering geometry. (1) An almost flat manifold $(M,g)$ must be flat if it is Einstein, i.e. $\operatorname{Ric}_g=\lambda g$ for some real number $\lambda$.…

We formulate the Gerstenhaber algebra structure of Hochschild cohomology of finite group extensions of some quantum complete intersections. When the group is trivial, this work characterizes the graded Lie brackets on Hochschild cohomology…