2024/11/10 by Joshua Howie, Dionne Ibarra, Howie, Joshua A. +5
Computer Science · #11R04 (Secondary) #53C27 #57K32 (Primary) 15A66 #Artificial Intelligence in Games #FOS: Mathematics #Geometric Topology (math.GT) #Mathematics, Computing, and Information Processing
paper · pdf · doi:10.48550/arxiv.2411.06368
openalex publication_date 2024/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the complete hyperbolic structure on the complement of the figure eight knot, we determine the set of lambda lengths from the maximal cusp to itself. Using the correspondence between spinors and spin-decorated horospheres, we show that these lambda lengths are precisely the Eisenstein integers, up to multiplication by a unit. We also show that the inter-cusp distances from the maximal cusp to itself are precisely the norms of Eisenstein integers.