Related papers: A Note on Closed G_2-Structures and 3-Manifolds

We present a proof of the fact that a closed orientable 4-manifold is parallelizable if and only if its second Stiefel-Whitney class, first Pontryagin class and Euler characteristics vanish. This follows from a stronger result due to Dold…

We have been interested in understanding the class of 7-dimensional closed and simply-connected manifolds in geometric and constructive ways. We have constructed explicit fold maps, which are higher dimensional versions of Morse functions,…

We show that every orientable 3-manifold is a classifying space B\Gamma where \Gamma is a groupoid of germs of homeomorphisms of R. This follows by showing that every orientable 3-manifold M admits a codimension one foliation F such that…

The recent mathematical literature introduces generalised geometries which are defined by a reduction from the structure group $SO(d,d)$ of the vector bundle $T^d\oplus T^{d*}$ to a special subgroup. In this article we show that…

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…

Let $G$ be a complex connected reductive algebraic group that acts on a smooth complex algebraic variety $X$, and let $E$ be a $G$-equivariant algebraic vector bundle over $X$. A section of $E$ is regular if it is transversal to the zero…

Let $M$ be a negatively curved compact Riemannian manifold with (possibly empty) convex boundary. Every closed differential $2$-form $\xi\in\Omega^2(M)$ defines a bounded cocycle $c_\xi\in C_b^2(M)$ by integrating $\xi$ over straightened…

We analyse the relationship between the components of the intrinsic torsion of an SU(3) structure on a 6-manifold and a G_2 structure on a 7-manifold. Various examples illustrate the type of SU(3) structure that can arise as a reduction of…

Computations based on explicit 4-periodic resolutions are given for the cohomology of the finite groups G known to act freely on S^3, as well as the cohomology rings of the associated 3-manifolds (spherical space forms) M = S^3/G. Chain…

We give several criteria on a closed, oriented 3-manifold that will imply that it is the boundary of a (simply connected) 4-manifold that admits infinitely many distinct smooth structures. We also show that any weakly fillable contact…

Among other things, we prove the following two topologcal statements about closed hyperbolic 3-manifolds. First, every rational second homology class of a closed hyperbolic 3-manifold has a positve integral multiple represented by an…

A compact 4-dimensional manifold is a non-singular graph-manifold if it can be obtained by the glueing T^2-bundles over compact surfaces (with boundary) of negative Euler characteristics. If none of glueing diffeomorphisms respect the…

In this paper we study a Hamiltonian function on the cotangent bundle of the space of Riemannian metrics on a 3-manifold $M$ and prove the orbits of the constrained Hamiltonian dynamical system correspond to $G_2$-manifolds foliated by…

We classify closed, simply-connected non-negatively curved 5-manifolds admitting an (almost) effective, isometric $T^3$ or $T^2$ action. As a direct consequence, we show that for any manifold, of dimensions up to and including 9 under the…

Every closed, oriented, real analytic Riemannian 3-manifold can be isometrically embedded as a special Lagrangian submanifold of a Calabi-Yau 3-fold, even as the real locus of an antiholomorphic, isometric involution. Every closed,…

We define new Riemannian structures on 7-manifolds by a differential form of mixed degree which is the critical point of a (possibly constrained) variational problem over a fixed cohomology class. The unconstrained critical points…

We study the types of non-integrable $\mathrm{G}$-structures on Riemannian manifolds. In particular, geometric types admitting a connection with totally skew-symmetric torsion are characterized. 8-dimensional manifolds equipped with a…

We first review the notion of a $G_2$-manifold, defined in terms of a principal $G_2$ ("gauge") bundle over a $7$-dimensional manifold, before discussing their relation to supergravity. In a second thread, we focus on associative…

We study the natural structure on the moduli space of deformations of compact coassociative submanifolds. We show that a G2-manifold with a T^4-action of isomorphisms such that the orbits are coassociative tori is locally equivalent to a…

We construct new compact manifolds endowed with closed $\mathrm{G}_2$ structures that satisfy the topological properties found by Joyce and Baraglia for the existence of a torsion-free $\mathrm{G}_2$ structure in the same cohomology class.…