Positive Ricci Curvature on Highly Connected Manifolds

Peer reviewed

Finite Group Actions on Kervaire Manifolds

Date of Acceptance: 09/06/2015

Immersions of Manifolds

Immersions of an m-manifold in an n-manifold, n>m, are classified up to regular homotopy by the homotopy classes of sections of a vector bundle E associated to the tangent bundle of M.  When N = Rn , the fibre of E is the Stiefel manifold of m-frames in n-space.

On imbedding differentiable manifolds in Euclidean space

Assume n,k,m,q are positive integers. Let M^n denote a smooth differentiable n-manifold and R^k Euclidean k-space. (a) If M^n is open it imbeds smoothly in R^k, k=2n-1 (b) If M^n is open and parallelizable it immerses in R^n (c) Assume M^n is closed and (m-1)-connected, 1< 2m-n < n+1. If a neighborhood of the (n-m)-skeleton immerses in R^q, a>2n-2m, then the complement of a point of M^n imbeds smoothly in R^q.

On embedding 4-manifolds in R^7

A compact, connected, combinatorial 4-maifold is embeddable in R^7 if its twisted normal Stiefel-Whitney class in dimension 3 is trivial.

On tubular neighborhoods of piecewise linear and topological manifolds.

Analogues of the smooth tubular neighborhood theorem are developed for the topological and piecewise linear categories.