2020/08/07 by Andrew Havens, Havens, Andrew, Robin Koytcheff +1 · 2 citations
Mathematics · Medicine · #57K10 #57K12 #57K35 #57R40 #57R50 #Algebraic Topology (math.AT) #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2008.03192
openalex publication_date 2020/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We recursively determine the homotopy type of the space of any irreducible\nframed link in the 3-sphere, modulo rotations. This leads us to the homotopy\ntype of the space of any knot in the solid torus, thus answering a question\nposed by Arnold. We similarly study spaces of unframed links in the 3-sphere,\nmodulo rotations, and spaces of knots in the thickened torus. The subgroup of\nmeridional rotations splits as a direct factor of the fundamental group of the\nspace of any framed link except the unknot. Its generators can be viewed as\ngeneralizations of the Gramain loop in the space of long knots. Taking the\nquotient by certain such rotations relates the spaces we study. All of our\nresults generalize previous work of Hatcher and Budney. We provide many\nexamples and explicitly describe generators of fundamental groups.\n