On differentiable manifolds with certain structures which are closely related to almost contact structure, I

Contact Structures on 5–manifolds

Using recent work on high dimensional Lutz twists and families of Weinstein structures we show that any almost contact structure on a 5–manifold is homotopic to a contact structure.

Contact Structures on 3–manifolds Are Deformations of Foliations

In this note we observe, answering a question of Eliashberg and Thurston in [2], that all contact structures on a closed oriented 3–manifold are C∞-deformations of foliations.

DIFFERENTIABLE STRUCTURES 1. Classification of Manifolds

(1) Classify all spaces ludicrously impossible. (2) Classify manifolds only provably impossible (because any finitely presented group is the fundamental group of a 4-manifold, and finitely presented groups are not able to be classified). (3) Classify manifolds with a given homotopy type (sort of worked out in 1960’s by Wall and Browder if π1 = 0. There is something called the Browder-Novikov-Su...

0 Cones and causal structures on topological and differentiable manifolds

General definitions for causal structures on manifolds of dimension d + 1 > 2 are presented for the topological category and for any differentiable one. Locally, these are given as cone structures via local (pointwise) homeomorphic or diffeomorphic abstraction from the standard null cone variety in IR d+1. Weak (C) and strong (C m) local cone (LC) structures refer to the cone itself or a manifo...

Notes on Differentiable Manifolds