Periodic Prime Knots and Toplogically transitive Flows on 3-Manifolds

Authors

William Basener, Rochester Institute of Technology
Michael C. Sullivan, Southern Illinois University CarbondaleFollow

Comments

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

Abstract

Suppose that φ is a nonsingular (fixed point free) C¹ flow on a smooth closed 3-dimensional manifold M with H₂(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).