Vol. 64, No. 1, 1976

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Homotopies and intersection sequences

John Robert Quine, Jr.

Vol. 64 (1976), No. 1, 233–240
Abstract

For γt : 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 (γt(z) γt(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
Authors
John Robert Quine, Jr.