Haefliger's approach for spherical knots modulo immersions

2021/10/26 by Gauniyal, Neeti
#57R40 #57R42 #58D10 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2110.13954

Abstract

We show that for the spaces of spherical embeddings modulo immersions Emb(Sⁿ,S^n+q) and long embeddings modulo immersions Emb_∂(Dⁿ,D^n+q), the set of connected components is isomorphic to π_n+1(SG,SG_q) for q≥ 3. As a consequence, we show that all the terms of the long exact sequence of the triad (SG;SO,SG_q) have a geometric meaning relating to spherical embeddings and immersions.

Related

• On the homotopy type of the spaces of spherical knots in Rⁿ
• Embeddings in the 3/4 range
• Isometric immersions of higher codimension into the product \mathbf S^k × H^n+p-k of sphere and hyperboloid
• On the Topological Structure Of Complex Tangencies to Embeddings of S³ into ℂ³
• Goussarov-Polyak-Viro type formulas for (4k-1)-dimensional knots and links in ℝ^6k