On knot invariants which are not of finite type

1999/03/10 by Theodore Stanford, Stanford, Theodore, Rolland Trapp +1
Mathematics · #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #math.GT #math.QA #msc:57M25

paper · pdf · doi:10.48550/arxiv.math/9903057

6 pages, no figures

arxiv created 1999/03/10 · arxiv updated 2009/11/30

Abstract

We observe that most known results of the form "v is not a finite-type invariant" follow from two basic theorems. Among those invariants which are not of finite type, we discuss examples which are "ft-independent" and examples which are not. We introduce (n,q)-finite invariants, which are generalizations of finite-type invariants based on Fox's (n,q) congruence classes of knots.

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