On spaces of connected graphs III: The Ladder Filtration
Abstract
A new filtration of the spaces of tri-/univalent graphs Bmu that occur in the theory of finite-type invariants of knots and 3-manifolds is introduced. Combining the results of the two preceding articles, the quotients of this filtration are modeled by spaces of graphs with two types of edges and four types of vertices, and an upper bound for dim Bmu in terms of the dimensions of the filtration quotients is given. The degree m up to which Bmu is known is raised by two for u=0 and u=2.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.