Topology of the space of locally convex curves on the 3-sphere

Emília Alves

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arXiv · 1608.04635

Topology of the space of locally convex curves on the 3-sphere

Emília Alves

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Abstract

A (positive) locally convex curve in the 2-sphere is a curve with positive geodesic curvature (i.e., which always turns left). In the 3-sphere, it is a curve with positive torsion. In this work we discussed the topology of spaces of such curves with prescribed initial and final jets. The case of the 2-sphere is understood (Saldanha-2013); the case of n=3 is not yet thoroughly clarified. In order to obtain partial information about the homotopy type of such spaces in the case n=3, we represented a positive locally convex curve as a pair of curves on the 2-sphere with some restrictions.

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BibTeX RIS

Emília Alves. 2016-08-16. Topology of the space of locally convex curves on the 3-sphere. https://arxiv.org/abs/1608.04635

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