Homotopies and intersection sequences

John Robert Quine, Jr.

Vol. 64 (1976), No. 1, 233–240

DOI: 10.2140/pjm.1976.64.233

Abstract

For γ_t : S¹ → C, a smooth homotopy of closed curves, the changing configuration of vertices and cusps is studied by considering the set in I ×S¹ ×S¹ given by (γ_t(z) −γ_t(ζ))∕(z −ζ) = 0. The main tool is oriented intersection theory from differential topology. The results relate to previous work by Whitney and Titus on normal curves and intersection sequences.

Mathematical Subject Classification

Primary: 57D35, 57D35

Milestones

Received: 5 November 1975

Revised: 24 February 1976

Published: 1 May 1976