2 6 D ec 2 00 6 Geometrical Theory on Combinatorial Manifolds ̧

2 6 D ec 2 00 6 Geometrical Theory on Combinatorial Manifolds ̧

ar X iv : m at h / 06 12 41 6 v 1 [ m at h . PR ] 1 4 D ec 2 00 6 An L 2 theory for differential forms on path spaces I

An L theory of differential forms is proposed for the Banach manifold of continuous paths on Riemannian manifolds M furnished with its Brownian motion measure. Differentiation must be restricted to certain Hilbert space directions, the H-tangent vectors. To obtain a closed exterior differential operator the relevant spaces of differential forms, the H-forms, are perturbed by the curvature of M ...

6 D ec 2 00 5 Generalised G 2 – manifolds Frederik Witt

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 generalise the notion of a manifold of holonomy G2, while the constrained ones give rise to a new geometry without a classical counterpart. We characterise these stru...

D ec 2 00 3 Non - orientable 3 - manifolds of complexity up to 7 Gennaro Amendola Bruno Martelli

We classify all closed non-orientable P-irreducible 3-manifolds with complexity up to 7, fixing two mistakes in our previous complexity-up-to-6 classification. We show that there is no such manifold with complexity less than 6, five with complexity 6 (the four flat ones and the filling of the Gieseking manifold, which is of type Sol), and three with complexity 7 (one manifold of type Sol, and t...

J an 2 00 3 COMBINATORIAL CONDITIONS THAT IMPLY WORD - HYPERBOLICITY FOR 3 - MANIFOLDS

Thurston conjectured that a closed triangulated 3-manifold in which every edge has degree 5 or 6, and no two edges of degree 5 lie in a common 2-cell, has word-hyperbolic fundamental group. We establish Thurston's conjecture by proving that such a manifold admits a piece-wise Euclidean metric of non-positive curvature and the universal cover contains no isometrically embedded flat planes. The p...