MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

2 added 22 characters in body

The following question is related to the Seifert conjecture.

Let $M$ be a closed manifold with zero Euler characteristic. Is it true that each homotopy class of nowhere-zero vector fields on $M$ contains a vector field with a finite number of (stable) limit cycles (closed trajectories)? Is it easy to construct?

1

# Existence of a vector field with a finite number of limit cycles.

The following question is related to the Seifert conjecture.

Let $M$ be a closed manifold with zero Euler characteristic. Is it true that each homotopy class of nowhere-zero vector fields on $M$ contains a vector field with a finite number of (stable) limit cycles? Is it easy to construct?