Results on the homotopy type of the spaces of locally convex curves on $\mathbb{S}^3$

DOI10.5802/aif.3267zbMath1456.57024arXiv1703.02581OpenAlexW2948063371MaRDI QIDQ2421937

Nicolau C. Saldanha, Emília Alves

Publication date: 18 June 2019

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.02581

zbMATH Keywords

homotopy typeBruhat decompositionlocally convex curves

Mathematics Subject Classification ID

Embeddings and immersions in topological manifolds (57N35) Classification of homotopy type (55P15) Curves in Euclidean and related spaces (53A04) Algebraic topology of manifolds (57N65) Homotopy and topological questions for infinite-dimensional manifolds (58B05)

Related Items (2)

Stratification of spaces of locally convex curves by itineraries ⋮ Locally convex curves and the Bruhat stratification of the spin group

Cites Work

• Flexibility for tangent and transverse immersions in Engel manifolds
• The classification of immersions of spheres in Euclidean spaces
• Nondegenerate curves on \(S^ 2\) and orbit classification of the Zamolodchikov algebra
• Existence \(h\)-principle for Engel structures
• Results on infinite-dimensional topology and applications to the structure of the critical set of nonlinear Sturm--Liouville operators
• Optimal paths for a car that goes both forwards and backwards
• The homotopy type of spaces of locally convex curves in the sphere
• Nondegenerate homotopies of curves on the unit 2-sphere
• On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents
• On the number of connected components in the space of closed nondegenerate curves on 𝑆_{𝑛}
• Partial Differential Relations
• TOPOLOGY OF THE SPACE OF NONDEGENERATE CURVES
• Immersions of Manifolds
• The geometry of spherical curves and the algebra of quaternions
• Spaces of Locally Convex Curves in S^n and Combinatorics of the Group B_(n+1)^+
• ON THE COMPONENTS OF SPACES OF CURVES ON THE 2-SPHERE WITH GEODESIC CURVATURE IN A PRESCRIBED INTERVAL
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Results on the homotopy type of the spaces of locally convex curves on $\mathbb{S}^3$