#### Abstract

Suppose that φ is a nonsingular (fixed point free) *C*^{1} flow on a smooth closed 3-dimensional manifold *M* with *H*_{2}(*M*)=0. Suppose that φ has a dense orbit. We show that there exists an open dense set *N* ⊆ *M* such that any knotted periodic orbit which intersects *N* is a nontrivial prime knot.

#### Recommended Citation

Basener, William and Sullivan, Michael C. "Periodic Prime Knots and Toplogically transitive Flows on 3-Manifolds." (Feb 2006).

## Comments

Published in

Topology and Its Applications, 153(8), 1236-1240.