On spaces of connected graphs III: The Ladder Filtration

Details On spaces of connected graphs III: The Ladder Filtration On spaces of connected graphs III: The Ladder Filtration

2003-01-03

arxiv.org/abs/math/0301020v1

Jour. of Knot Theory and its Ramif. vol. 10, no. 5 (2001), 675-686

Mathematics

Quantum Algebra

12 pages

Scientific paper

A new filtration of the spaces of tri-/univalent graphs B_m^u 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 B_m^u in terms of the dimensions of the filtration quotients is given. The degree m up to which B_m^u is known is raised by two for u=0 and u=2.

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