MathDB
Parallelizable manifolds

Source: Miklós Schweitzer 2018 P11

November 18, 2018
topology

Problem Statement

We call an mm-dimensional smooth manifold parallelizable if it admits mm smooth tangent vector fields that are linearly independent at all points. Show that if MM is a closed orientable 2n2n-dimensional smooth manifold of Euler characteristic 00 that has an immersion into a parallelizable smooth (2n+1)(2n+1)-dimensional manifold NN, then MM is itself parallelizable.