• Corpus ID: 119294158

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

@article{Alves2016TopologyOT,
  title={Topology of the space of locally convex curves on the 3-sphere},
  author={Em'ilia Alves},
  journal={arXiv: Geometric Topology},
  year={2016}
}
  • E. Alves
  • Published 16 August 2016
  • Mathematics
  • arXiv: Geometric Topology
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… 
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